Ignore Blue, he obviously hasn't thought it out
(Seriously though Blue, Dual Wielder?
No-one takes Dual Wielder for DPR. It adds at most an average of +1. Two-Weapon Fighting? Adds + Mod to
one attack.)
By itself a TWF Oathbreaker Paladin matches up with a GWF when neither have advantage (although I think advantage swings it towards the GWF).
Between Improved Divine Smite and Aura of Hate, you're stacking 1d8+Cha mod onto every hit, so a free bonus action attack each turn is just gravy. Add even more sources of +Cha mod onto that?
Yeah, you do great damage. And are somewhat original for a Paladin.
You probably want to go Strength based though, so you can focus those two stats.