Oath of Conquest
Everybody wants to rule the world.
Spells
Some real windfalls, however Spiritual Weapon Doesn't work with Smites. Speaking of which, smites still deal extra damage to undead and fiends, weird for an "evil" Paladin.
Channel Divinity
A fear or +10 to hit on one attack. Better than Abjure Enemy, and worse than Sacred Weapon.
Aura of Conquest
Makes your Channel Divinity Fear more useful. Kind of weak compared to other auras.
Implacable Spirit
Now you are immune to charm, way later than a devotion paladin would get it, who also gets protection from evil at this level giving them even more immunities. Other Paladins get cooler things like not dying or a use for their reaction.
Invincible Conqueror
Finally something to dominate the battlefield. An extra swing per attack, resistance to everything, and bonus critical hit range. Barbarians wish they had a rage that good.
Possibly the best capstone for Paladins so far, too bad it's a Capstone.
Thoughts:
Smites being tied to banishing undead and fiends is weird. The Spells are good, the features are rather underwhelming. Except maybe the part where they can inflict fear and keep it going for a long time, that's at least mechanically interesting, perhaps a more palatable and less obtrusive way to introduce something akin to marking. Basically a Controller in playstyle, an odd pick for something that is supposed to be a Conqueror. Maybe it's just me but "conqueror" implies a person who is more competent in fighting a war than being a bully. Perhaps I expected something more like a reverse-warlord.
Oath of Treachery
Not quite faithless. This is more like someone who couldn't cut the mustard instead of someone who was betrayed by the things they swore an oath to.
Spells
You are really good at running away and hiding. Also a smattering of charm for some reason. Haste is the real combat booster here.
Channel Divinity
Conjure Duplicate You are your [-]own best[/-] only friend, or alternatively the sock-puppet account. It's mechanically interesting, you can use it to cast spells (even though none of your spells make very good use of that feature) or give yourself advantage.
Poison Strike Now this is a good idea for a traitor. Unfortunately it's anti-synergistic. You want to get advantage, but can't get it via your duplicate because they use the same limited resource. Also, if you actually do manage to get advantage, you lose the benefit of having damage dice instead of flat bonus damage, meaning your Crits actually get weaker for your trouble!
Aura of Treachery
Cull the Herd This is how you get advantage without your Duplicate. Unfortunately, it makes using your duplicate that much more questionable due to the fact that advantage is the only tangible benefit of using the duplicate.
Treacherous Strike This is really fun. Too bad it only works within 5'. It really should be tied to whatever attack triggered it, melee reach breaks all kinds of abilities that it really has no right to be breaking. Or just let it apply to any attack, using your enemy (or a victim) to block an arrow aimed at you is a tried and true narrative beat that demands to be catered too.
Blackguard’s Escape
So you are really good at running away. HOWEVER the thing is you are still a paladin, likely rocking some heavy armor with a movement speed of 20' so you aren't going to get away. Meaning you want to use this to set up a second ambush. HOWEVER the thing is you are still a paladin, likely rocking some heavy armor with no real DEX bonus so you aren't going to be able to use the hide action. Meaning you are only going to use this to get advantage on an attack. HOWEVER the thing is you are a paladin, with the Oath of Treachery so you have a plethora of redundant ways to set up advantage. Meaning this ability is simply a free teleport as a reaction to get some better positioning.
Icon of Deceit
This is another really good capstone.
Basically it's "you get 20 extra damage on all of you attacks, also you can make the enemy hit themselves when they hurt you"
Well in theory it's really good, in reality you are invisible so things are going to have the damnedest time trying to hurt you.
Thoughts:
Anti-synergies abound, this Oath is it's own worst enemy. A fitting fate for a traitor, but not as fun as it could be to actually play as.