Overlooking the Obvious: Hexadin Smite/Smite Build

On one hand, Paladins and Warlocks are, traditionally, radically opposed to one another flavor-wise. A Paladin is a solemn servant of a higher power whose strengths are bound up in an oath they swear to fulfill their quest. A Warlock has made a deal to gain personal power, often compromising morals and even their own future in order to receive power from entities that might be purely malevolent.

Of course, the existence of Celestial (as well as some good Archfey, and even good Undying in Eberron) patrons and the existence of darker shades of Paladin like the Oath of Conquest or even the Oathbreaker (officially designed for villainous NPCs, but playable at the DM's discretion) means that these two classes aren't necessarily as far from one another as one might think.

Mechanically, as well, both are Charisma-based spellcasters, which adds more of an opportunity for some effective multiclassing.

But what really takes the cake is Smites. Smiting is one of the defining features of the 5E paladin, letting them expend spell slots once they've hit something to do extra damage. One of the ways that make the Divine Smite feature so powerful is that you don't have to choose whether to do so until you know that you've hit - you never waste a spell slot unless it's just going to do way more damage than you needed to kill the thing.

Even more excitingly, Smites can crit, and again, you can wait until you've landed the crit to decide whether to smite. So if you're feeling like there's a 20 on your way (maybe your Divination Wizard friend foresaw it, or you've racked up advantage, or the target's paralyzed or unconscious - though in the latter case you probably don't need the damage) you can hold onto your smites and make them deal twice the damage.

Following? Ok:

Divine Smite does not require any additional action - you can do it any time you land an attack, be that your post-level-5 extra attack, an opportunity strike, or a bonus from great weapon master or haste. This also means that you can use it any number of times per turn as you have spell slots to burn.

Warlocks who go with the Pact of the Blade can take an invocation called Eldritch Smite. This allows you to spend a spell slot when you hit with a melee attack and deal an additional d8 of Force damage per spell level of the slot, as well as automatically knocking it prone if it's not gargantuan in size (like Repelling Blast, this is one of those fun "you can't save against this, it just happens" things Warlocks can do.)

Effectively, it recreates Divine Smite for Warlocks, though it's slightly less powerful in terms of raw damage (both do cap out at 5d8, though Paladins' Divine Smite can be boosted up to 6d8 if the target is a fiend or undead.)

Combining these two features might look, on its surface, redundant. You could just go pure Warlock and take Eldritch Smite if you want that gameplay, or you could just dip a little into Warlock - enough to get two spell slots - and just be happy to have two short-rest-recharging Smite Slots.

But here's where it gets insane:

Remember how there's no action required to smite? It just happens when you hit something, immediately, and with no reaction or bonus action or any of that crap?

Well, there's nothing saying that you can't use both Eldritch Smite and Divine Smite on the same attack.

Let's imagine a level 10 Paladin/Warlock. Say they're Vengeance/Hexblade+Pact of the Blade. The Hexblade half lets you use Charisma for both casting and attacks, and Pact of the Blade opens up any sort of weapon you want - take a Greatsword, for example. Also, you've got Hexblade's Curse, which allows you to crit on 19s, meaning you have a 1/10 chance to crit (and if you have advantage, that makes it just under 1/5 of a chance... technically it's a 19%).

Now, you swing at the big bad... dracolich, and you roll a 19 on your cursed target, letting you crit.

So, already you've got 4d6 from the greatsword crit. You then roll in your 2rd level Divine Smite, which deals 8d8 (2 baseline, 1 more for level of the slot, and 1 because it's undead, all doubled) followed by a 3rd level Eldritch Smite, dealing 6d8 (again, doubled for crit.)

That means you're dealing 4d6 + 14d8 damage (plus your charisma modifier and your proficiency thanks to Hexblade's curse.) The dice damage, then, is an average of 77, and it's knocked prone, giving you advantage for your next attack, which you have by this level.

And, of course, if you had used your bonus action to put on one of the various spell-smites on top, that gets doubled as well.

Not terrible for a single attack.