Percy can communicate with sea creatures. This may seem a bit odd for the Avengers at first, but it could actually be very useful. Sea creatures could act as scouts in areas near water, providing the Avengers with early warnings of approaching threats. Also, some sea creatures have healing properties themselves, and Percy could potentially use his connection with them to find new ways to heal the Avengers.
As time goes on, Percy would start to train with the Avengers. He would learn their fighting styles and they would learn about his powers. He might have some funny moments with Thor, comparing their abilities related to water and lightning. Percy would also form close bonds with the more compassionate Avengers like Captain America, who would be very interested in Percy's ability to heal.
Another possibility is that the girl is sent to the Avengers world as a sort of test by a powerful being. She has to prove herself worthy by assisting the Avengers in saving the world from a new and dangerous villain. Along the way, she forms close bonds with the different members of the team. She might teach Thor some new tricks from her world, or learn combat skills from Black Widow.
Another option could be Black Widow. She's very good at adapting to new situations and using her skills in different ways. For Percy, who is coming from a very different world, she could teach him how to be stealthy and use his powers in a more covert way. She could also help him with understanding the political side of the Avengers, like dealing with government agencies and such, which Percy may not be used to in his world of demigods.
Well, it could go either way. If the writer wants to create an interesting twist, Percy might be a villain in the Avengers fanfiction. But more often than not, given Percy's own heroic traits from his original story, he'd probably be a hero in the Avengers' universe, helping the Avengers fight against their common enemies.
Percy has his speed and agility. In the fanfiction, he might be able to use his demigod reflexes to dodge all of the Avengers' attacks. He could then quickly move in for a counter - attack. Also, his sword, Riptide, is a powerful weapon. It can cut through almost anything. He could use it to cut through the Avengers' weapons or their defenses if he gets close enough.
She could become a new member of the Avengers. Suppose she has a super - intelligence. She could help Tony Stark in his research, coming up with innovative solutions to upgrade their weapons and technology. This would make her a valuable addition to the team, and she would gain the respect of the other Avengers over time.
Iron Man would be angry. He'd probably use his technology to try and track Percy down. He might also start to review all the security protocols to make sure no other traitors could do the same. Thor would be more of the 'let's fight him head - on' type, but the other Avengers would have to hold him back until they have a proper strategy.
Well, initially, the Avengers would be quite skeptical. I mean, they deal with high - tech and super - soldier stuff. But once Percy shows what he can do, like summoning a giant sea monster to help in a battle, they'd start to see the value. Iron Man would likely try to find a scientific explanation for Percy's powers and might even try to replicate them in some way. Captain America would appreciate Percy's courage and how he uses his powers for good, just like he does with his own abilities.
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.