I love the idea of two-weapon fighting, and tinkering around with it. My character is going to be a Paladin. But to effectively dual wield as a Paladin I need to delve into either Ranger or Fighter, unless the DM is gracious and gives me Two-Weapon Fighting Style instead of the Paladin's normal choices. For the purposes of this question, we will assume that isn't the case.
Paladin 12 / Fighter 8 is the final build. Only going up to 12 in Paladin for the automatic divine weapon smite 1d8 bonus on damage attacks and the ASI. I'll be doing Vengeance for Hunter's Mark, adding another 1d6 per attack. Assuming Dual Wielder Feat, an attack should be roughly 2d8 + 1d6 + mod, which is relatively decent in my eyes considering you do that 3 times per round + occasional smiting on critical hits.
For Fighter at level 3 I would be going Eldritch Knight for bonding weapons and more spell slots.
This is where things can get a bit fun, and a bit iffy. From what I have read, wielding a heavy weapon in one hand gives disadvantage on attack rolls. Using the 2nd level spell Enlarge, you then pull out two bad ass heavy weapons and proceed to two-weapon style with them.
Honestly this is completely up to DM ruling and whatnot. For example PHB p. 147:
Two-Handed. This weapon requires two hands when you attack with it.
Based on that alone you could overrule having a greatsword in each hand, even when under the effects of enlarge. Becoming a size category larger would make sense that you could wield heavier weapons though, for the same reasoning small creatures can't use heavy weapons all that great but medium can. Enlarge only lasts for 1 minute, and requires concentration, so if you fail a concentration saving throw to maintain it you are now stuck with two huge weapons you can't really use, forcing you to switch back to regular ones.
Another question would be does the added 1d4 damage apply to the greatswords.
The target’s weapons also grow to match its new size. While these weapons are enlarged, the target’s attack with them deal 1d4 extra damage.
Would switching to the greatswords beforehand add in the extra damage? Or would they now be even bigger and your new size unable to wield them anyway? I could always switch to the greatswords after the spell has been cast. In either case, could this work?