Well, a plot could be that Godzilla's appearance in the Evangelion world is part of a grand experiment by SEELE. They want to see how the Evas and the world of Evangelion will adapt to this new threat. The pilots are then caught in the middle of this experiment. Or perhaps Godzilla's radiation has an unexpected effect on the Evas, making them mutate in strange ways. This would force the pilots to deal with not only a huge external threat but also the internal changes in their own mechas. Another idea is that Godzilla starts to bond with one of the Eva units, like Unit - 01. This creates a very unique situation where Shinji has to work with Godzilla instead of just fighting it, and they end up becoming an unexpected force against the Angels.
A possible plot idea is that Godzilla is drawn to the Geo - Front in Evangelion. The reason could be the powerful energy sources there. The NERV organization is then forced to either work with Godzilla or find a way to get rid of it. They might study Godzilla's biology to see if they can use any of its abilities to enhance the Evas. Another plot could be that an Angel takes on the form of Godzilla to deceive the Eva pilots. This would make the pilots question their usual tactics when facing an 'Angel' as Godzilla has different strengths and weaknesses compared to the normal Angels. Also, a plot where Godzilla's presence causes a shift in the power dynamics between the different factions in Evangelion, like SEELE and NERV, could be really interesting.
One plot idea could be that the Dragon Balls are accidentally brought into the Evangelion universe. This causes a stir as different factions in the Evangelion world, like NERV and SEELE, try to get their hands on them for their own purposes. Meanwhile, the Z - Fighters follow the Dragon Balls and end up in this strange new world. Another idea is that an Eva unit gains the ability to use ki, like a Saiyan. This Eva then goes rogue and starts causing chaos, and it's up to both the Evangelion pilots and the Z - Fighters to stop it.
One idea could be an Evangelion and Gundam crossover. Picture the Eva units in a battle alongside Gundam mechas against a common enemy. Another could be a crossover with Neon Genesis Evangelion and Sailor Moon. The pilots of the Evas could meet the Sailor Scouts and combine their powers to fight a new threat. And a third idea might be an Evangelion and Pokémon crossover, where the Angels are somehow related to powerful Pokémon and the Eva pilots have to use Pokémon in addition to their Evas to save the day.
One idea could be a Godzilla crossover with King Kong. They could start off as enemies but then have to team up to fight a common, greater threat like an alien invasion. This would bring in the classic monster -vs- monster dynamic at first and then shift to an alliance against a new foe.
How about a Godzilla crossover with the Avengers? Maybe in a world where the Avengers exist alongside the Kaiju. Godzilla could be seen as both a threat and an ally. Iron Man could try to study Godzilla's power source while Thor might see him as a kind of primordial force. Captain America would be the one trying to keep everyone in line and figure out how to co - exist with this giant monster.
One idea could be Godzilla teaming up with other kaiju from different universes to fight a common, powerful enemy. Maybe an alien force that is threatening all kaiju-kind.
One idea could be that Godzilla somehow ends up in Equestria. The ponies are initially terrified but then realize Godzilla is more interested in protecting the land from some new dark force that has emerged there. Maybe Godzilla's size and power are a mystery to the ponies at first, and Twilight Sparkle tries to study him to figure out how he got there.
One idea could be that Godzilla arrives in the RWBY world due to a strange rift in dimensions. The Huntsmen and Huntresses initially see Godzilla as a huge threat and try to fight it. But then they discover that Godzilla is actually there to fight a common enemy, like a new type of Grimm that is immune to normal attacks but vulnerable to Godzilla's atomic breath.
A Godzilla and Evangelion crossover would be cool. Godzilla could be the ultimate Third Impact scenario that the Evangelion units have to face. It would be a battle of titanic proportions with the mechs trying to take down the giant lizard using their unique weapons and Godzilla's raw power overwhelming them at times.
One idea could be that Godzilla Earth teams up with a group of humans who have developed advanced technology to fight off an alien invasion. The humans initially fear Godzilla but soon realize they need his power.
It could be about Godzilla emerging in the world of Evangelion. Maybe the Angels in Evangelion are confused by this new giant monster. The Eva pilots might have to deal with both Angels and Godzilla at the same time.