Well my DM rules (and some sage advice indicates) that being on a spell list makes something a spell for that class. So my Warlock/Eldritch Knight has Truestrike, Agonizing Green Flame Blade and Eldritch Blast from being a 6th level Warlock, but Truestrike and GFB are "Wizard spells" and therefore work with Warmagic. EB is not and if I cast EB I do not get to attack. She is a Tiefling and also has Firebolt, which is again a "Wizard spell"
If that's what your DM rules, cool. With the potential of using a heavy weapon with Great Weapon Master, I, however, do not see a major benefit in having Eldritch Blast on this build, though. Instead of investing in Charisma on top of Intelligence, you could just invest in Strength. And with the new rules involving heavy weapons requiring a minimum strength score of 13 and Full Plate requiring a Strength score of 15, this build gets quite mad. If you dump Intelligence and just get spells without save or attack roll via Eldritch Knight and do everything else via Warlock, it gets a bit easier. If you want more damage, going the Strength route is better. If you more higher level spells, multiclassing into Wizard is better after level 7.
Yeah so this is fine, but the way I do it is use Action Surge first (nefore you take your action), attack and then cast a spell with your action to get the benefit of Eldritch Strike.
That certainly allows you to cast a leveled spell beyond 2nd level and really benefits your build because we multiclassing into Warlock, you may not get Improved War Magic.
I also don't really like either Haste or Mind Sliver, there are better spells. For a cantrip something with more damage, for a 3rd level spell something with more effectiveness and no downside when it ends.
You generally cast Mind Sliver for the d4 debuff which stacks with other debuffs like Bane. I'd use it depending on how important it is to me that my next spell lands. If you really want to hit with Dissonant Whispers and the target is a CR 17 Death Knight with a +9 to Wisdom saves and Advantage on saves against spells, just Disadvantage won't cut it. And a CR 17 Death Knight is just barely a deadly encounter for 4 level 12 characters. But fortunately, their Intelligence save is just +1 and just right for the Mind Sliver debuff.
And yeah, Death Knights are immune to the frightened condition as well, but fortunately, Dissonant Whispers doesn't use the Frightened condition. Command would work as well here and might even be better if you want to burn the targets turn.
If damage is more important, Toll the Dead works too and you don't need Spell Sniper for it when casting it in melee as you would for Firebolt, for example.
At level 11+ I really like the combo I mentioned above:
Action Surge: Truestrike or Blade Cantrip, attack, attack
Action: Dissonant Whispers (save with disadvantage)
Reaction: Truestrike
Bonus Action: Wrathful Smite (save with disadvantage)
Since Dissonant Whispers doesn't trigger the second part of Booming Blade according to Jeremy Crawford, this still works really nicely, especially against melee only characters. And in all other cases, Booming Blade deals more damage than True Strike (d8 vs d6). If 3rd party material is allowed, Vengeful Blade can also be a nice option against casters.
And since Dissonant Whispers isn't on the Wizard spell list, you'd have to do it that way anyway because it doesn't work with Improved War Magic.
IF I am going to use a 3rd level slot I really like Fear:
Action Surge: attack-attack-nick attack-blade cantrip make these attacks all against different people
Actoion: Fear (anyone who got hit on the attack action saves with disadvantage)
With the right positioning, that can work quite well as long as you're not in a campaign with a lot of immunity to the Frightened condition. That, of course, requires that you still fight hordes of creatures at that level which isn't too common.
I would not consider playing either of those subclasses without a multiclass.
Fortunately for you, you don't have to. But Valor Bard with Shillelagh or a Lute of Thunderous Thumping, if you can get your hands on it, works quite well. But 2 levels of Warlock really improve the damage output, true. In that case, I would start with Warlock, though, because, while Dex saves are more frequent, Wisdom saves usually are worse and being paralyzed or charmed isn't fun.
I think a Goblin Enchantment Wizard is the most powerful single-classed full caster generally from level 2-20. They are not the strongest at every one of those levels, but they are generally the strongest overall when you consider all of those levels.
I assume you refer to 2014 rules since all classes now get their subclasses at level 3. I was really surprised to hear that, because you don't hear somebody stand up for enchanters very often. For a good reason!
Enchantment isn't bad, but I don't think they even come close to Chronurgy at any level. In fact, if consider the exploits Necromancy Wizards can do with Inured to Undeath, Create Magen, Aid, and Heroes' Feast plus how they change the action economy, how valuable Divination Wizards can be, not just with Portent but with having nearly infinite spell slots to figure out where the party needs to go, what the new Illusion Wizard can do, particularly at level 14 which can lead to default kills if used right, the new Bladesinger which is nearly unkillable if played right, I wouldn't even rank them a top 5 subclass. And when I consider Peace Clerics, Twilight Clerics, or Eloquence Bards, Enchanters don't make the cut either.