Yes, there are quite a few. Some fanfictions manage to blend the powers and characters from Percy Jackson's world, like Percy's demigod abilities, with the superheroes in the Avengers. They create really interesting storylines where they might team up to fight a common enemy or face off in a battle of ideologies.
You can try Archive of Our Own (AO3). It has a large collection of fanfictions, and you're likely to find some great 'godlike Percy Jackson Avengers' ones there. Just use the search function and type in relevant keywords.
Yes, there are some fanfictions out there that attempt to combine the Harry Potter concept of the Master of Death with the Naruto universe. Some authors are really creative in finding ways to blend the magic systems, like how the Deathly Hallows might be equivalent to certain ninja tools or jutsus. However, the quality can vary a great deal from one fanfic to another.
In some fanfictions, the settings are merged. So you might have Camp Half - Blood with a touch of Hamilton - era architecture or the characters from Hamilton having to deal with the monsters from Percy Jackson's world. The values of loyalty and friendship from Percy Jackson can also be contrasted with the power - hungry and ambitious nature of some Hamilton characters, creating really interesting storylines that are more than just the sum of their parts.
Yes, there are some fanfics out there that attempt to blend the 'Game of Thrones' and 'Attack on Titan' universes. However, the quality can vary greatly. Some may focus on bringing the political intrigue of 'Game of Thrones' into the world of 'Attack on Titan', while others might have characters from one series interacting with those from the other in unique ways.
There could be. A good fanfic would probably focus on the unique aspects of each universe and find a way to blend them. For example, the magic system in Harry Potter and the Devil Fruit powers in One Piece. It might start with a magical accident that transports a character from one world to the other and then explore how they adapt and interact with the new environment.
The characters could interact in various ways. For instance, Percy might be a bit in awe of Thor's lightning powers at first but then realize that his own water powers can also be extremely powerful in different ways. The Avengers might be intrigued by the concept of Greek gods being real in the Percy Jackson universe. They could team up to fight a common enemy that somehow threatens both their worlds. Maybe a villain who wants to use the power of the Greek gods and also the Infinity Stones. In such a scenario, the combined strength of both groups would be necessary to save the day.
One way is through character crossovers. For example, Percy Jackson could meet Kratos from God of War. Percy's water - based powers would contrast with Kratos' brute strength. Maybe they could team up against a common enemy like a powerful sea monster that has been influenced by the Greek gods in a way that also ties to the dark mythology of God of War.
One way to combine the two universes could be through a portal. Imagine Percy Jackson accidentally stumbling upon a magical portal while on a quest near the ocean. This portal leads him to the world of Pirates of the Caribbean. He could then team up with Jack Sparrow, using his demigod powers to help Jack in his adventures, like fighting Davy Jones' crew. Maybe Percy's ability to control water could be a great asset during sea battles.
Well, in fanfiction, it could also be that there is a common enemy. For example, a powerful ancient being that is a threat to both the demigod world of Percy Jackson and the world that Agents of Shield operates in. This would force them to team up. Percy's powers like controlling water could be really useful in some of the situations that Agents of Shield faces, like dealing with underwater threats or putting out fires in a unique way.
The two universes blend in various ways. In fanfiction, Percy's powers can be adapted to the Skyrim setting. His ability to control water can be used in Skyrim's many waterways. Also, the mythology of Percy Jackson can be merged with Skyrim's lore. For example, the gods in Percy's world could be compared or even interact with Skyrim's divines.