They could be amused. It's like seeing a mirror of their world but with a school - based twist. They might like the creativity behind it.
They might find it really interesting. It could be a strange experience for them to see their own world and adventures reimagined in a fan - made story set in a school environment. They might laugh at some of the creative liberties the fanfic author took or be impressed by how accurately some aspects were captured.
They might react with surprise. Fanfiction often has very different takes on their characters and stories.
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.
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.
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.
The demigods could have a range of reactions. Some might enjoy seeing different interpretations of their world and relationships. For example, if a fanfiction focuses on a friendship that a demigod values, they might feel happy that others also find it interesting. Mortals would likely be excited. They would be immersed in the fantastical elements of the PJO universe as presented in the fanfiction, and it could inspire them to read the original books if they haven't already.
It can influence readers by teaching them values. For instance, the loyalty shown by demigods can make readers value their own relationships more. The courage of the characters can inspire readers to be brave in their own lives.
Some of Percy's school friends might be completely bewildered. They see these strange - looking kids (the demigods) showing up and whisking Percy away. They could be left standing there with their mouths open, not really understanding what just happened.
One important aspect could be loyalty. In PJO fanfiction, characters often face difficult choices that test their loyalty to their friends, their godly parents, or their camps. Another aspect is courage. Demigods are constantly in dangerous situations, and seeing how they summon the courage to face their fears can be a great moral lesson. Also, the concept of sacrifice. Many times, demigods have to sacrifice their own desires or safety for the greater good.