One possible plot could be that in a world where the gods of Percy Jackson and the Avengers co - exist, Percy is somehow tricked or forced to banish the Avengers. Maybe there's a power struggle among the gods and they see the Avengers as a threat to their power, so they use Percy, who has a strong connection to the divine world, to get rid of them. Percy might be conflicted as he may admire the Avengers' heroism but has to follow the gods' orders.
Well, perhaps the god in question has been misusing their powers and causing harm to mortals and demigods alike. Percy, being the hero he is, decides to take matters into his own hands and banish the god. After the banishment, Percy then has to find a way to fill the void left by the god. He might have to take on some of the god's former responsibilities, which is no easy feat as he is still just a demigod.
One possible plot could be that the gods in the Percy Jackson universe sense a great threat from another dimension (the Marvel universe). Percy and his friends are sent to team up with the Avengers. Percy's water powers could be useful in fighting villains like Electro. Annabeth's strategic mind would assist in planning battles against foes like Loki. They all have to learn to work together, with Percy and the Avengers initially having some clashes due to their different ways of handling things.
It could be Ares. He is often portrayed as a violent and unpredictable god. Percy might banish him if he goes too far in causing wars and chaos among mortals. His banishment would have a huge impact on the battlefields of the mortal world.
Percy would be really conflicted. On one hand, he's used to following the orders of the gods, but on the other, he knows the Avengers are heroes. He'd probably feel guilty about banishing them. The Avengers would be confused and angry. They'd try to figure out who Percy is and why he's banishing them. Iron Man might try to use his technology to find a way out of the banishment, while Captain America would be more focused on trying to reason with Percy.
One possible plot could be that the Avengers mistake Percy for a threat. Maybe they see his powers with water and think he's some kind of new, unknown enemy. They capture him to figure out what he is. Percy, of course, would be confused and probably a bit angry at being wrongly accused.
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 possibility could be that Percy, being the banished son of Odin, has to prove himself in the world of Percy Jackson. Maybe he has powers from Odin that are not fully understood in the demigod world. He could go on a journey to discover his true identity and find a way to regain his place. For example, he might face challenges from both the Norse and Greek mythological beings. He may have to use his wits and newfound powers to overcome these obstacles.
In some fanfictions, Percy might be banished because he goes against the traditional ways of the demigod society too much. For example, if he tries to form an alliance with a group that the other demigods consider enemies. His actions could be seen as a threat to the stability of their world, so they banish him to keep the peace.
Well, he might face a lot of challenges. Alaska is a cold and harsh place. He could encounter new mythical creatures that are native to that region in the fanfiction. Maybe he has to find a way to survive the extreme cold while also dealing with any enemies that banished him there in the first place.
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.