I'm building a world for a new campaign, and I'm looking into ways for all the gods of this multiverse to have existed up to a point, and then all be gone. Currently I'm exploring just a single Wish spell, cast by an NPC with a grudge against the gods. How possible/believable/likely do you think it would be for a Wish such as "I wish the gods were gone" to cause somewhere around a dozen gods to simply no longer exist?

Another option I've looked at is several Imprisonment spells, each cast for a different deity, but this would require each one to fail a save, which seems insanely unlikely. Or perhaps I could just homebrew some sort of powerful ritual, done in secret, that either imprisoned or banished the gods. Thoughts?

I'd go with gods getting irritated that a mortal thinks he can get away with such foolishness. Because they are upset, they leave that mortal and his country to their own devices, suffering from bad weather, poor crops, clerical spells not working - all the effects that would suggest the Wish worked but the gods are merely taking a step back and having people suffer for their arrogance.

For all the deities to disappear, something extremely epic would have to occur.  A Wish spell has rather limited parameters compared to the powers of most deities.  Think about it: a Djinn can grant Wishes.  So can Efreeti.  If Wishes could wipe out gods, wouldn't these warring factions of have wiped each other out with Wish spells a long time ago?  Wouldn't some Archdevil have wished the demons out of existence after getting their hands on a Wish spell?  

If you want to homebrew a spell that can kill gods, I suggest considering components and  rituals that are similarly titanic in scale.  Think about what wiped out the dinosaurs.  You can't do that with a Meteor Swarm or even a hundred Meteor Swarms.  That's the difference between general mortal magic (even 20th level) and god-level magic.

I would probably twist the Wish. Like, the gods aren’t gone, but are now all trapped in a modified Imprisonment spell or now their plane can no longer interact with the prime material plane.

I have a similar game where the majority of the gods are dead due to a very powerful ritual by a school of wizards hoping to take their place. Unfortunately for them, things didn’t work out to plan and now the stability in the planes is eroding and the universe is naturally seeking new beings to take up the mantle of the gods. Which is great when good humanoids get ahold of it. Less great when illithids get ahold of these god genesis artifacts, mwahahaha. 

As said above, you are the final arbiter of the world. But maybe it wasn't wish, but like a super wish or urwish spell, lost to the passage of time. Maybe the spell destroyed all of the gods, but the universe interpreted him, by wielding that magnitude of power as a sort of a god and destroyed him too, and in such a way that made it nearly, if not actually, impossible to follow in his footsteps.

I would, in such a case, have fragments of weird left around, to show the revealed faultlines of existence after such an event. Maybe there are areas where reality warps unexpectedly, or certain regions where space was compressed-- the sort of thing you'd expect to see in Numenera. After all, such an event would be a catacylsm of cosmic significance.

I'm reminded of the case of the Lady of Pain, a being powerful enough to forbid the gods, but who deals out extreme punishment to anyone worshiping her lest she become one and be banished as well.

Very unlikely. If any djinn or lv. 17 wizard could destroy the entire pantheon, it'd be long gone already. But here's a couple other potential ways they could disappear. Remember that, no matter what happens, a god is on a power scale so far beyond mortals that anything capable of wiping them all out should be the most powerful force in existence

1. Dawn War: The Primordials might have shown up and wrecked shit up. This is how the gods disappeared from the Dark Sun setting, although it would likely cause some massive upheaval, if not in the Prime Material, definitely in the Astral Sea and Elemental Chaos (although you wouldn't really notice any difference in the Chaos). If the players travel to the Astral Plane at some point, they'd likely find it in complete chaos, with aftermath of the war being clearly visible, deific corpses floating all over the place.
2. Lack of Belief: It might be a bit unlikely that an entire world would become atheists at once, but Gods Need Prayer Badly, and if people stop believing in them, they disappear. In Magic: The Gathering, planeswalker and all around dickbag Nicol Bolas accomplished this by killing every adult on the entire plane of Amonkhet.