Is 4/0 wire overkill for to run from the battery to the inverter or is 0 gauge enough? The unit will be about 3ft from my battery bank.

Thicker cable is always better. You want to use a minimum of 0 awg cable on all four terminals and connect all 4 to the same battery even if multiple batteries are present. If you want to add (optional) an inline fuse, they should be rated at 250 Amps each on both of the positive cables, near the battery.