First, welcome to the boards!
I'm going to give a rules-as-written reading, fully aware that most DMs wouldn't care at all given the way you've tricked out your fighter.
The basics have been covered, and the list from pdegan is perhaps clearest. There are just a few small nuances I'd like to point out:
Since you took two-weapon fighting as your style, your off-hand attacks will roll the same as your main hand, so you can probably arrange with the DM to balance your multi-attack rounds more between your two hands if you want. This may become useful down the stretch if you happen to pick up a pair of magic swords with effects that trigger on a hit, you'll want to make sure the off-hand weapon's effect gets plenty of chances to trigger.
Technically, there no longer is "off-hand" attacks. That is to say, when you take the attack action, you can use either weapon in either hand. If you've only used one weapon in the attack action, the bonus attack can be made with the other hand.
This becomes relevant after level 5 if there are magical properties on different weapons (let's say "flame" and "frost", both being non-heavy, since you have the feat; light if you didn't; we could equally say piercing and bludgeoning or whatever).
With extra attack, Attack action lets you attack twice. It can be with flame, or frost, or one with each.
If both those attacks are with a single weapon (e.g. flame), you meet the criteria for two weapon fighting (which requires the attack action to use only one hand and one weapon), using frost.
If you then use Actionsurge, it can be with either flame or frost (but no bonus action, since you've attacked that way already).
So a level 5 TWF fighter using action surge could make
* 2 fire 1 frost 2 fire attacks
* 2 fire 1 frost 1 fire 1 frost
* 2 fire 2 frost [bonus and the first attack of the surge] 1 fire
* 2 fire 3 frost
* 1 fire 1 frost 2 fire 1 frost [saving the bonus until the end, riding the surge]
* 1 fire 3 frost 1 fire [bonus at end]
* 4 fire 1 frost [bonus at end]
* 1 fire 1 frost 1 fire 1 frost [but no bonus action, since no attack action used only one weapon]
* 3 fire 1 frost [no bonus]
(or any of the above nine possibilities, swapping fire and frost and vice versa).
But you can't make:
* 1 fire 2 frost 1 fire 1 frost
* 1 fire 2 frost 2 fire
* 5 fire
* 3 fire 2 frost
* 1 fire 1 frost 1 fire 1 frost 1 fire.
(or again any of these swapping fire for frost, swapping fire for frost)
Is that all the permutations? I think so.
Ultimately, though, You're pretty flexible, and have a lot of options, and most tables won't care one way or another.
I'm seeking to buff twfing for the fighter. Even with up to +3 weapons, twfing falls behind gwfing in damage right at level 5 (due to action surge). Maybe on hit magic weapons boost it enough.
To this, I would suggest that not everyone cares about DPR, and that it is perfectly possible to enjoy D&D without maximizing damage.
DPR in this case, though, is positively misleading -- TWF gives you flexibility, and the ability to move onto additional targets as you wish after each roll of the die, which means that the damage you are doing is much more efficiently applied than it would be with two great weapon attacks.
Both are completely legitimate approaches, but it is wrong to say that falling behind in average damage means anything in actual play: the type of opponents you are facing, their number, and whether you have magic weapons (and whether they are light, or heavy), and whether they do different types of damage, are all relevant variables that simply cannot be controlled by theorizing alone.
Stick with your character, and have fun.