Percy would probably find it hilarious. He has a good sense of humor and would likely enjoy the wild and crazy scenarios fans come up with. He might even share the funnier ones with his friends at Camp Half - Blood.
Some characters might be flattered. Like Percy, he could be happy to see that people are so interested in his story in 'The Son of Neptune' that they write fanfiction about it.
Grover would be a bit more cautious. He might be a bit scared of the Norse monsters at first. But as he reads more, he'd start to see the similarities between the Norse and Greek worlds in terms of how nature is involved. He might notice how the Norse also have a connection to the natural world, like the wolves and the trees, and how it compares to his own connection to nature in the PJO universe.
For demigods, it could either reinforce their existing views or introduce new perspectives. If a fanfiction delves deeper into a certain aspect of their world like the powers of a god, they might gain a new understanding. Mortals would have a more comprehensive view of the PJO world. They would learn about different characters and their backstories that might not be fully explored in the original books.
It can be considered common. There are a large number of PJO fans out there, and fanfiction is a popular medium in fan communities. Since the official books have a set storyline, fanfiction offers a chance to expand on it, so many 'mortals' (fans) are attracted to it.
One great 'pjo avengers crossover fanfiction' is 'The Demigod Avengers'. It has an exciting plot where the demigods from Percy Jackson and the Olympians join forces with the Avengers. The character interactions are really well - written, like when Percy uses his water powers in a fight alongside Thor's lightning.
One benefit is that it allows you to explore different interpretations of the original PJO world. Fanfiction often takes the existing characters and settings and twists them in new and interesting ways. It can also give you a deeper connection to the fan community as you share in the creativity of fellow fans.
A big theme is also about power and responsibility. As a mercenary, Percy has power in his skills and abilities, but he also has the responsibility to use them for good. In many fanfictions, he struggles with how far he can go in his mercenary work without compromising his values. For example, he might be offered a large sum of money to do something that goes against his moral code, and how he deals with that is a central part of the story. This theme is explored in different ways in different fanfictions, sometimes more subtly and sometimes more directly.
One tip is to know the original PJO series well. This helps you understand the characters' personalities and backstories in the fanfiction. Another is to explore different platforms where fanfictions are hosted. Some might have better quality stories. Also, don't be afraid to try different genres of fanfiction, like adventure or romance set in the PJO universe.