A common theme is the clash of different power systems. Thor's godly powers from Asgard are very different from the powers of DC heroes. Fanfics often explore how these powers interact, like Thor's lightning against Superman's heat vision.
I also like 'Thor Among the DC Heroes'. In this story, Thor is kind of lost in the DC universe and has to find his way back home. Along the way, he meets various DC characters like Batman, and their interactions are very well - written. The author does a great job of showing how Thor's brashness contrasts with Batman's more calculated nature.
Another idea is that Greninja gets exposed to some kind of meta - human - creating substance in the DC universe and gains new powers. It could then join the Teen Titans, sharing its unique Pokémon abilities with the group. It would be interesting to see how Greninja interacts with characters like Robin, Starfire, and Cyborg, and how it uses its powers in battles against the Titans' enemies.
I'm not sure if there is such a specific fanfiction. But if it exists, it might be a really wild crossover. Maybe Naruto somehow gets the powers of Thor from DC and has to use them in the Naruto universe. For example, he could use Mjolnir instead of his kunai and shuriken, and his Rasengan could be infused with lightning like Thor's powers.
A crossover could start with Wonder Woman being summoned to Asgard by some mysterious magic. She finds herself in a strange new world and is initially met with suspicion. Thor, being the more open - minded of the Asgardians, decides to help her figure out how she got there. Along the way, they discover that an ancient enemy from Thor's past has plans to use Wonder Woman's power to open a portal to a realm full of chaos. They then have to work together to stop this from happening, with Wonder Woman teaching Thor some new combat techniques she learned on Themyscira and Thor showing her the power of the Asgardian magic.
Definitely Marvel. Thor has been a key figure in Marvel comics for a long time. His adventures and storylines are all part of the Marvel comic universe's rich tapestry.
Well, in a Naruto and Thor crossover fanfic, maybe Naruto is on a journey and accidentally stumbles into a portal that leads him to Asgard. There, he meets Thor. Thor is intrigued by Naruto's tenacity and ninja skills. They could exchange their combat techniques. Naruto shows Thor how to move stealthily like a ninja, and Thor teaches Naruto some of his Asgardian battle tactics. And together they could face a threat to Asgard that is related to some dark chakra - like magic that has seeped into Asgard from another dimension.
Character consistency. Thor should still be recognizable as his Marvel self even in a different crossover world. For example, his strength, his sense of honor and his hammer - wielding abilities should be intact.