Best use for the new melee cantrips?

[Spacehamster]

3 levels paladin 17 levels arcane trickster, dueling style, your one attack gets weapon damage, cantrip damage, smite damage and sneak attack damage?

[Corran]

Throw divine favor (or hunter's mark if OoV) on top of that.
Cons: You have one chance to deliver sneak attack, and limited spell slots with which to smite.

Usually the best way to use the new cantrips is under the conditions that trigger their secondary effect. They can also mitigate the need for the extra attack feature for specific multiclass characters and allow for more flexible multiclass builds.

[Gignere]

Tome lock 3 light patron from UA, draconic sorcerer 6, Oathbreaker 7, Assasin 3, Last level can be anything.

Shillelagh, green flame blade - you get to quintuple dip charisma on an attack, auto crit + sneak attack and smites.

[Corran]

you get to quintuple dip charisma on an attack
How's that?

[Gignere]

How's that?
Light patron lock + cha to fire damage, draconic sorcerer + cha to fire damage, Oathbreaker + cha to melee damage, Shillelagh use cha to hit and damage, GFB adds cha to second targets damage. Quintuple dip cha in one attack.

[Lonely Tylenol]

Checks out, but I have to question whether the extra three dips into caster stat are worth the level investment (and the loss of things like scaling sneak attack) that it entails, given that none of the CHA mod stuff critically strikes. For example, the extra 5 levels in Paladin could net you 6 more levels in Assassin (with that unassigned last level) for an extra +3d6 against the 1d8+5 of CHA-enhanced smite (and more uses, which is certainly a check in favor of this build). If you save your smites for assassinates, you will be doubling up on 1d8 (Shillelagh) + 2d8 (Divine Smite, 1st-level spell) + 3d8 (Greenflame Blade) + 5d6 (Sneak Attack) before adding the triple CHA mod. Better nova, I'd wager, but perhaps weaker round-to-round--but you also get Expertise, Uncanny Dodge and Evasion, for what that's worth.

EDIT: You could achieve the same thing by taking out all 6 levels of Sorcerer instead of Paladin, and keep the round-by-round consistency Paladin might afford, at the expense of adding CHA to both the primary and secondary targets.

EDIT II: Sorcerer's probably still better because of how multiclassing works with spell slots.

EDIT III: With the benefits conferred by Quicken Spell out of the Sorcerer metamagics, the five levels in Paladin are probably still more worthwhile than an equal number of levels in Rogue for the nova, because you can use your Attack action with an extra attack and then bonus action Greenflame Blade.

[EvanescentHero]

I'm pretty sure you can't stack the same bonus multiple times unless explicitly stated.

[Z3ro]

I'm pretty sure you can't stack the same bonus multiple times unless explicitly stated.

I thought the opposite was true in this edition; unless stated everything stacks.

[silveralen]

I'm pretty sure you can't stack the same bonus multiple times unless explicitly stated.

It never says that. It mentions prof, but the rulebook never otherwise says anything.

[Foxhound438]

3 levels paladin 17 levels arcane trickster, dueling style, your one attack gets weapon damage, cantrip damage, smite damage and sneak attack damage?

it's even better if you have them in hold person