I'm not a fan of the Illrigger. But it's mostly because I can see what it -could- have, and maybe should have, been.
1) The Name
Illrigger. What an absolutely terrible name. It has no cultural connection, no linguistic derivation, it's a whole cloth creation to define the class... Which I kinda get. Sometimes words don't exist and you have to punch them into reality with all the violence your fingers can muster against a keyboard. But -this- one is just awful. Not only do you -have- to know that there's going to be racists that change out one of the Rs because it's a double G and hard R, the first 3 require a capitalization that makes them look like a roman numeral of 3.
Structurally the term fits the mouth just fine, particularly with the way it pulls your lips back for the initial il and ri sounds. But it lacks any sort of punch in the way it rolls out. It's hard to find a stressed syllable so it's a very flat sound in my mind. Ultimately there are much better extant words that would fit the class better. Especially with the concept being what it is:
2) Narrow Concept
It's a Hellknight. You don't need to create a new 'more generic' term to describe the class on the precept that there's a lot of different cultural ways to be a hellknight. That's why "Fighter" is so open a term rather than miring it into a concept like "Knight" or "Gladiator". Because it's this broad concept that can easily slot into a variety of situations you need a broad term. Illrigger does not have this issue. It is a Hellknight.
And because it is a hellknight, and one defined exclusively by it's relation to the 9 lords of hell, it's got an incredibly narrow shelf-life of archetypes, 5 of which are already written. Sure, later on you can try to wedge things open a bit wider but you've kinda written yourself into a corner at the start. The Warlock is written to be open ended to touch on various sources of power and even though there's an infernal patron you could always take the time to make individual patrons of each lord of hell for the warlock and still have room to do every major demon, archfey, and elder god in a given setting.
3) Awful Name for the "Interdicts"
Interdiction means to "Prohibit". Baleful Interdict means "To Prohibit in an Evil Way". But -why- go for Interdict at all when Maledict or "Evil Word" is -right there-?! You could even call the class Malefactor and have their seals be Maledictions and have their name be an "Evildoer" who "Says Evil Things". 90% of people don't know what interdict means and are gonna have to look it up in a dictionary. And what are you prohibiting, anyhow? That's not how the seals -work-. They don't seal anything. They're just marks on your target that your interdict boons (Prohibition Benefit?) trigger off of.
Honestly, it's maddening.
4) Seals have minimal effect
Pretty much the only reason to put a seal on a target is to break it almost immediately. They last for an hour if they're not burned, but burning them is how you make them -do- something. At level 1 you put a seal on a target and -as soon- as someone else hits them you burn it to gain an extra 1d6 damage. You can do this 3 times per short rest and... that's it. At level 2 you get interdiction (prohibition) which grants you a single minor benefit either if you burn a seal off a target or if you expend a seal that was never on a target (costing you 1d6 of damage). The only boon you get early on that gives you a reason not to instantly burn your seal off a target allows you to get a free Opportunity Attack once per round that doesn't take your reaction... but with how comparatively rare opportunity attacks and reactions even -are- you don't really need it. Especially since burning the seal doesn't eat your reaction! So what are you even saving your reaction for? Someone ELSE to try and move away without disengaging?
5) Combat is Short
Outside of specific encounter structures combat tends to cap out between 3-4 rounds just because of the amount of damage players and enemies can swing around. So you're gonna throw a seal on turn 1 (either by hitting or bonus action), burn it before turn 2 most likely, possibly throw another to burn in the second or even third round... And then beg for a short rest like a Warlock chucking all their spell slots in the first 2 turns. And while I agree that makes synergy between the Warlock and the Hel- sorry 'Illrigger' pretty strong... I just feel like it's a poor use of the fantasy. Better to have the seals actually -do- something so that you aren't putting them on just to burn them off at your earliest opportunity.
6) Seals don't do anything on their own.
Better to put a seal on a character at the start of the fight that causes some kind of prohibition for its duration and then you burn it in an effort to end them once your seal is no longer useful to you. Imagine a Seal that makes ranged combat dangerous for the person the seal is on, so they have to close to melee. THEN you burn the seal to deal damage while keeping them pressed in melee so they can't get back to range. That would be -way- more evocative and interesting as a battlefield mechanic than throwing it onto a target and burning it ASAP.
And it would give you a reason NOT to burn seals, but to hold onto an active seal and move it to another target once the first one hits 0HP.
So how do you fix this?
1) Better name.
I like Malefactor pretty well. It's broad and generic enough to encapsulate a lot of concepts, but I feel like it might be -too- broad, since a Malefactor can be an armored knight or a robed cultist or an assassin in the night. We need something that evokes a sort of pseudo-historical quasi-medieval role. Preferably one that, like Barbarian, Rogue, and Warlock, doubles as an oft-used insult in concept. After all, the Romans referred to anyone who didn't speak latin as a Barbarian because their words sounded like "Bar Bar Bar Bar" to the Roman ear. Rogue itself is a demeaning term only slightly removed from the more directed term thief in that it describes a general cad and person of low character. While Warlock is meant, of course, to evoke mages working in league with evil forces compared to the term Wizard which is somewhat more neutral in it's descriptive power.
So how about Knave? It's a word that has a specific low character, it's an insult, and it is also an alternative to "Jack" in a deck of cards giving it a face-value of 11 that sets it aside from most of the other cards. It's also right up there with "Varlet" for insults that knights shout at each other before crashing into each other in an honor duel, with the Knave or Varlet being the transgressor the duel is about. It's a real world historical term that puts it into the right time period but is broad enough as a concept (Unscrupulous Person) that many cultures have their own knaves.
2) Broader Concept
Obviously with a better name you get the broader concept. No longer is this just a hellknight, it's instead a bigger, more open, concept. But how to handle slotting it into the D&D narrative? Well. Firstly, the illrigger is basically designed to be a hell based antipaladin in the most blatant way possible. They even get "Invoke Hell" instead of Channel Divinity. But if we're going to broaden them from hellknights to allow them to be servants of various dark powers and twisted entities rather than a strict hellknight, we need something broader.
If a Paladin is a Cleric/Fighter, why not make the Knave a Warlock/Fighter? So now instead of a single hierarchy of Hell to bow to, you've got a broader grouping of potential power sources: Patrons. But if we do those as archetypes, won't we just be making a bladelock class? It's definitely a possibility. So what if your Patron is a flavor-bonus rather than your Archetype? But, then, what does your archetype become?
3) Archetypes as How, not Why
When D&D24 was coming up I lamented moving the Patron to level 3 for Warlocks. I think it's a terrible design decision made exclusively to make a specific mechanical balance that cares nothing for narrative elements. It's a decision that Tales of the Valiant took and ran with, too, which makes Warlocks into the weakest character class of the hybrid caster types in that game at level 1. Worse armor, Worse HP, Worse damage than either the Ranger or the Paladin at level 1 without any sort of commensurate benefit to make them good at anything in particular. In the search for balance at low levels they made the Warlock the worst at level 1.
So leave the Patron as a ribbon at level 1. Make the Archetype be -how- you serve your patron. Are you a hellknight in heavy armor? Get it at 3rd. Are you a marauder on the high seas tossing souls overboard to appease Davy Jones? Get benefits for it at 3rd. Do you command a legion of pixie warriors? Get it at 3rd. You get the idea. And that way you can be the Feyknight, too. Or the commander of a legion of demons or devils or aberrations.
4) Seals become Curses
Paladins swear an oath. Knaves swear a blue streak! Interdictions become Maledictions! Give them -Curses- instead of Seals. It plays into the occult vibes of patrons and it better fits into the idea of prohibitions. It also serves as a great mechanical basis for keeping your effects going on targets and a pile of potential curses can be found in any Magic Item list. "Curse of Arrow Attraction", for example, to make a target easier to hit with ranged attack rolls (Your party Ranger and Warlock will thank you) "Curse of the Berserk" to throw onto an orcish commander before someone hits him with a ranged attack forcing a Wisdom Save or he's going to whallop his nearest target which might be a minion or it could be the shaman providing magical support to his soldiers! Heck, throw out multiple curses onto the same target to -really- grind them down with different problems they have to navigate to really ruin their day. Or spread them across multiple foes and burn them all to ash.
Plus "Curse" or "Malediction" is a better name than "Baleful Interdict" and you could "Break Curses" for damage rather than "Burning Seals". And hey, your "Interdiction Boons" can just become "Invocations" to match the naming convention of Warlocks since you're kinda tying the classes together, conceptually, this way. Better names all around!
5) Change a few more names.
"Infernal Conduit" is going to need a change of name since they're no longer strictly hellknights. But nothing about moving hit dice from yourself to allies or stealing health from enemies is, strictly speaking, 'hellish' anyhow. So let's change out the Infernal part. Could go for "Vampiric Conduit" to make it more blood-centric... but then again you've got the Bloodhunter really trying to corner the market on the more sanguine terms. So how about Conduit of Death? After all, whether you're serving a Fey Patron or some Deathgod or an Angel you're a warrior type and you're mostly going to be used to kill things.
Sure, you're using those hit dice of yours to heal people, but isn't that just channeling some of their impending death into yourself to avoid them dying? Personally I'm less a fan of "Your only method of healing also rips you apart", myself, so I'd also change the mechanics a little bit to reflect that... Especially since Bloodhunter, again, has the "Self Harming Combatant" thing down as a core class element. Hand of the Master can replace Infernal Majesty (though you still get resistance and flight). And maybe instead of "Master of Hell" (which when you're strictly a minion of hell is a weird naming flex) we can go for "Open the Way" for the big damaging magic attack and make it portal-centric though where the portal leads is more patron-specific. I did stick with blood for one of their abilities, though: The burning HD for save bonuses has a good concept for a Bloody Resolve.
Et voila. A class that has a better name, a broader concept base, more room for individual characterization, and plays with the same "Apply and Burn" mechanic in a way that is likely more conducive to group-play and not tearing through all your "Interdicts" in a single fight.
Why, yes, I did write it up as a Level Up/A5e instead of D&D24 or 5e class. But that's just because I prefer A5e. You could slot "Combat Mastery" right back in at 2nd level and make them use Extra Attack at 5th level instead of a more tailored 'Quasi-Eldritch Blast' knave's strike improvement, but... y'know.
The spirit of things is the point. What it could be instead of what it is.
1) The Name
Illrigger. What an absolutely terrible name. It has no cultural connection, no linguistic derivation, it's a whole cloth creation to define the class... Which I kinda get. Sometimes words don't exist and you have to punch them into reality with all the violence your fingers can muster against a keyboard. But -this- one is just awful. Not only do you -have- to know that there's going to be racists that change out one of the Rs because it's a double G and hard R, the first 3 require a capitalization that makes them look like a roman numeral of 3.
Structurally the term fits the mouth just fine, particularly with the way it pulls your lips back for the initial il and ri sounds. But it lacks any sort of punch in the way it rolls out. It's hard to find a stressed syllable so it's a very flat sound in my mind. Ultimately there are much better extant words that would fit the class better. Especially with the concept being what it is:
2) Narrow Concept
It's a Hellknight. You don't need to create a new 'more generic' term to describe the class on the precept that there's a lot of different cultural ways to be a hellknight. That's why "Fighter" is so open a term rather than miring it into a concept like "Knight" or "Gladiator". Because it's this broad concept that can easily slot into a variety of situations you need a broad term. Illrigger does not have this issue. It is a Hellknight.
And because it is a hellknight, and one defined exclusively by it's relation to the 9 lords of hell, it's got an incredibly narrow shelf-life of archetypes, 5 of which are already written. Sure, later on you can try to wedge things open a bit wider but you've kinda written yourself into a corner at the start. The Warlock is written to be open ended to touch on various sources of power and even though there's an infernal patron you could always take the time to make individual patrons of each lord of hell for the warlock and still have room to do every major demon, archfey, and elder god in a given setting.
3) Awful Name for the "Interdicts"
Interdiction means to "Prohibit". Baleful Interdict means "To Prohibit in an Evil Way". But -why- go for Interdict at all when Maledict or "Evil Word" is -right there-?! You could even call the class Malefactor and have their seals be Maledictions and have their name be an "Evildoer" who "Says Evil Things". 90% of people don't know what interdict means and are gonna have to look it up in a dictionary. And what are you prohibiting, anyhow? That's not how the seals -work-. They don't seal anything. They're just marks on your target that your interdict boons (Prohibition Benefit?) trigger off of.
Honestly, it's maddening.
4) Seals have minimal effect
Pretty much the only reason to put a seal on a target is to break it almost immediately. They last for an hour if they're not burned, but burning them is how you make them -do- something. At level 1 you put a seal on a target and -as soon- as someone else hits them you burn it to gain an extra 1d6 damage. You can do this 3 times per short rest and... that's it. At level 2 you get interdiction (prohibition) which grants you a single minor benefit either if you burn a seal off a target or if you expend a seal that was never on a target (costing you 1d6 of damage). The only boon you get early on that gives you a reason not to instantly burn your seal off a target allows you to get a free Opportunity Attack once per round that doesn't take your reaction... but with how comparatively rare opportunity attacks and reactions even -are- you don't really need it. Especially since burning the seal doesn't eat your reaction! So what are you even saving your reaction for? Someone ELSE to try and move away without disengaging?
5) Combat is Short
Outside of specific encounter structures combat tends to cap out between 3-4 rounds just because of the amount of damage players and enemies can swing around. So you're gonna throw a seal on turn 1 (either by hitting or bonus action), burn it before turn 2 most likely, possibly throw another to burn in the second or even third round... And then beg for a short rest like a Warlock chucking all their spell slots in the first 2 turns. And while I agree that makes synergy between the Warlock and the Hel- sorry 'Illrigger' pretty strong... I just feel like it's a poor use of the fantasy. Better to have the seals actually -do- something so that you aren't putting them on just to burn them off at your earliest opportunity.
6) Seals don't do anything on their own.
Better to put a seal on a character at the start of the fight that causes some kind of prohibition for its duration and then you burn it in an effort to end them once your seal is no longer useful to you. Imagine a Seal that makes ranged combat dangerous for the person the seal is on, so they have to close to melee. THEN you burn the seal to deal damage while keeping them pressed in melee so they can't get back to range. That would be -way- more evocative and interesting as a battlefield mechanic than throwing it onto a target and burning it ASAP.
And it would give you a reason NOT to burn seals, but to hold onto an active seal and move it to another target once the first one hits 0HP.
So how do you fix this?
1) Better name.
I like Malefactor pretty well. It's broad and generic enough to encapsulate a lot of concepts, but I feel like it might be -too- broad, since a Malefactor can be an armored knight or a robed cultist or an assassin in the night. We need something that evokes a sort of pseudo-historical quasi-medieval role. Preferably one that, like Barbarian, Rogue, and Warlock, doubles as an oft-used insult in concept. After all, the Romans referred to anyone who didn't speak latin as a Barbarian because their words sounded like "Bar Bar Bar Bar" to the Roman ear. Rogue itself is a demeaning term only slightly removed from the more directed term thief in that it describes a general cad and person of low character. While Warlock is meant, of course, to evoke mages working in league with evil forces compared to the term Wizard which is somewhat more neutral in it's descriptive power.
So how about Knave? It's a word that has a specific low character, it's an insult, and it is also an alternative to "Jack" in a deck of cards giving it a face-value of 11 that sets it aside from most of the other cards. It's also right up there with "Varlet" for insults that knights shout at each other before crashing into each other in an honor duel, with the Knave or Varlet being the transgressor the duel is about. It's a real world historical term that puts it into the right time period but is broad enough as a concept (Unscrupulous Person) that many cultures have their own knaves.
2) Broader Concept
Obviously with a better name you get the broader concept. No longer is this just a hellknight, it's instead a bigger, more open, concept. But how to handle slotting it into the D&D narrative? Well. Firstly, the illrigger is basically designed to be a hell based antipaladin in the most blatant way possible. They even get "Invoke Hell" instead of Channel Divinity. But if we're going to broaden them from hellknights to allow them to be servants of various dark powers and twisted entities rather than a strict hellknight, we need something broader.
If a Paladin is a Cleric/Fighter, why not make the Knave a Warlock/Fighter? So now instead of a single hierarchy of Hell to bow to, you've got a broader grouping of potential power sources: Patrons. But if we do those as archetypes, won't we just be making a bladelock class? It's definitely a possibility. So what if your Patron is a flavor-bonus rather than your Archetype? But, then, what does your archetype become?
3) Archetypes as How, not Why
When D&D24 was coming up I lamented moving the Patron to level 3 for Warlocks. I think it's a terrible design decision made exclusively to make a specific mechanical balance that cares nothing for narrative elements. It's a decision that Tales of the Valiant took and ran with, too, which makes Warlocks into the weakest character class of the hybrid caster types in that game at level 1. Worse armor, Worse HP, Worse damage than either the Ranger or the Paladin at level 1 without any sort of commensurate benefit to make them good at anything in particular. In the search for balance at low levels they made the Warlock the worst at level 1.
So leave the Patron as a ribbon at level 1. Make the Archetype be -how- you serve your patron. Are you a hellknight in heavy armor? Get it at 3rd. Are you a marauder on the high seas tossing souls overboard to appease Davy Jones? Get benefits for it at 3rd. Do you command a legion of pixie warriors? Get it at 3rd. You get the idea. And that way you can be the Feyknight, too. Or the commander of a legion of demons or devils or aberrations.
4) Seals become Curses
Paladins swear an oath. Knaves swear a blue streak! Interdictions become Maledictions! Give them -Curses- instead of Seals. It plays into the occult vibes of patrons and it better fits into the idea of prohibitions. It also serves as a great mechanical basis for keeping your effects going on targets and a pile of potential curses can be found in any Magic Item list. "Curse of Arrow Attraction", for example, to make a target easier to hit with ranged attack rolls (Your party Ranger and Warlock will thank you) "Curse of the Berserk" to throw onto an orcish commander before someone hits him with a ranged attack forcing a Wisdom Save or he's going to whallop his nearest target which might be a minion or it could be the shaman providing magical support to his soldiers! Heck, throw out multiple curses onto the same target to -really- grind them down with different problems they have to navigate to really ruin their day. Or spread them across multiple foes and burn them all to ash.
Plus "Curse" or "Malediction" is a better name than "Baleful Interdict" and you could "Break Curses" for damage rather than "Burning Seals". And hey, your "Interdiction Boons" can just become "Invocations" to match the naming convention of Warlocks since you're kinda tying the classes together, conceptually, this way. Better names all around!
5) Change a few more names.
"Infernal Conduit" is going to need a change of name since they're no longer strictly hellknights. But nothing about moving hit dice from yourself to allies or stealing health from enemies is, strictly speaking, 'hellish' anyhow. So let's change out the Infernal part. Could go for "Vampiric Conduit" to make it more blood-centric... but then again you've got the Bloodhunter really trying to corner the market on the more sanguine terms. So how about Conduit of Death? After all, whether you're serving a Fey Patron or some Deathgod or an Angel you're a warrior type and you're mostly going to be used to kill things.
Sure, you're using those hit dice of yours to heal people, but isn't that just channeling some of their impending death into yourself to avoid them dying? Personally I'm less a fan of "Your only method of healing also rips you apart", myself, so I'd also change the mechanics a little bit to reflect that... Especially since Bloodhunter, again, has the "Self Harming Combatant" thing down as a core class element. Hand of the Master can replace Infernal Majesty (though you still get resistance and flight). And maybe instead of "Master of Hell" (which when you're strictly a minion of hell is a weird naming flex) we can go for "Open the Way" for the big damaging magic attack and make it portal-centric though where the portal leads is more patron-specific. I did stick with blood for one of their abilities, though: The burning HD for save bonuses has a good concept for a Bloody Resolve.
Et voila. A class that has a better name, a broader concept base, more room for individual characterization, and plays with the same "Apply and Burn" mechanic in a way that is likely more conducive to group-play and not tearing through all your "Interdicts" in a single fight.
Why, yes, I did write it up as a Level Up/A5e instead of D&D24 or 5e class. But that's just because I prefer A5e. You could slot "Combat Mastery" right back in at 2nd level and make them use Extra Attack at 5th level instead of a more tailored 'Quasi-Eldritch Blast' knave's strike improvement, but... y'know.
The spirit of things is the point. What it could be instead of what it is.