I think the interaction between Hulk and Grover would be fascinating. Grover is this gentle, nature - loving satyr, and Hulk is, well, the big green rage - monster. Grover could try to use his empathy and nature powers to soothe the Hulk, which could lead to some really comical and heartwarming moments. Also, Natasha Romanoff and Clarisse would be an interesting duo. Natasha's stealth and combat skills combined with Clarisse's brute force and no - nonsense attitude could make for some great fight scenes and character development.
One interesting interaction could be between Percy and Tony Stark. Percy, being used to a more mythological world, might be fascinated by Stark's high - tech gadgets. Stark, on the other hand, could be intrigued by Percy's ability to control water. They might start off bickering about whose powers are better but then end up respecting each other.
Definitely Percy and Eragon. Percy with his quick - witted and brave nature would have an interesting dynamic with Eragon, who is more solemn and duty - bound. They could learn a lot from each other, like Percy teaching Eragon about having a sense of humor even in tough situations, and Eragon showing Percy the importance of loyalty to a cause.
Definitely Loki. In a 'Percy Jackson and Avengers crossover fanfiction', Loki would find Percy's world of Greek gods and demigods fascinating. He could try to use Percy's knowledge of the gods to his own advantage, or maybe even form an unlikely alliance with Percy. Loki's mischievous nature would add a whole new layer of chaos and intrigue to the crossover.
Another interesting interaction would be between Annabeth and Tony Stark. Annabeth is highly intelligent and strategic, much like Tony. They could either be in a battle of wits, constantly trying to one - up each other in terms of coming up with plans, or they could end up working together really well. Annabeth could teach Tony about ancient Greek architecture and strategy, while Tony could show her some of his latest high - tech inventions.
I think the interaction between Percy and Chase would be really interesting. Percy has his quick - thinking and his water powers, while Chase is the smart one in the Lab Rats with his super - intelligence bionic ability. They could have some great debates about strategy and technology vs. magic.
Definitely Kakashi and Percy. They are both protagonists in their own right, and seeing how their different personalities interact would be fascinating. Percy is impulsive and has a strong sense of justice, while Kakashi is more reserved and calculating.
One possible plot could be that the Greek gods, noticing the powerful threats the Avengers face, send Percy Jackson and his friends to help. Percy could use his water powers to assist in putting out fires during a battle like the one in New York. Meanwhile, Thor could be intrigued by Percy's connection to Poseidon and they could exchange stories about their godly fathers.
One way could be to have Percy Jackson's powers of being a demigod interact with the superpowers of the Avengers. For example, his ability to control water could be used in a joint mission with Thor's lightning powers. Maybe they are facing a common enemy that can only be defeated by combining their unique skills.
Ikaris and Thor would be really interesting. Ikaris has his flight and laser - like eye powers, while Thor has his godly strength and control over lightning. They could have a friendly competition over who can reach a far - off location faster or who can defeat more enemies in a short time. Their different personalities, with Ikaris being more stoic and Thor being more boisterous, would create great banter.
Definitely Spider - Man and Iron Man. Iron Man could be like a mentor to Spider - Man, upgrading his suit and giving him advice on how to handle big - time villains. Another great interaction would be between Spider - Man and Captain America. Their different outlooks on responsibility and heroism could create some really interesting dialogue.