How to beat Vesta Overkill?

Stinger-style drones are non-issue, unless intercepting very fast (in which case it's not testable, as I can't at the same time guide attacking drones and defending ship) - their exit velocities are low, so my ships (up to and including gunship and fleet carrier counterparts) can dodge incoming fire. If this fails, their armour is lighter than usual, but hardening and stuffing still allow it to deflect and absorb punishment quite effectively - the ships can typically reorient to face what it cannot dodge quite rapidly, and failing that single drone pelting from something like stock stingers/hellfires that's being actively dodged is unlikely to penetrate in more than 1-2 odd places. And there are also lasers.

As for nukes, all my radiators and external armour skin are refractory, while crew is positioned to optimally resist spin, additionally, the ships have auxiliary RTGs and can be run in low signature mode while firing decoys, and still have power for last ditch chemgun CIWS. I had my ships slapped by a whole flight of devastators and remain combat worthy - good KKVs are much more problematic than nukes.

Do note that all my ships so far have been limited to vanilla reactors, and all my ships on the workshop are 100% stock modules - that's quite limiting, nevertheless my gunship counterpart (Dragon), when manually guided can take on 5 gunships at gun range and, with a bit of skill, avoid taking any damage while beating them (granted, that's using protective missile screen, and exploiting gunship's crap aluminum CM radiators).