Well, he might meet some really tough Norse warriors. Maybe he'd get into some epic battles or challenges. He could also make new friends or enemies among the Norse gods and heroes there.
If Percy Jackson goes to Valhalla in fanfiction, he could meet a whole bunch of Norse heroes. There's Sigurd, the dragon - slayer. And then there are the Valkyries who choose who gets to go to Valhalla. He might also run into Loki, who is always causing some sort of trouble. Percy would be in for quite an adventure as he tries to figure out who he can trust among these new and often unpredictable characters.
In this type of fanfiction, it's a really interesting concept. One possible scenario could be that Percy's death is a heroic sacrifice. Maybe he gives his life to save the world from an even greater threat than before. And when he becomes a god, he might use his new powers to bring about a new era of peace among the gods and demigods. His transformation could also mean changes in his relationships. For example, his friends might now have to view him in a different light, as a divine being rather than just a fellow demigod.
In this fanfiction scenario, Percy's adaptation to Hogwarts would be a complex process. He'd first have to deal with the cultural shock of a new magical world. The Hogwarts houses would be different from the cabins at Camp Half - Blood. He'd need to figure out which house he belongs in. His skills with a sword might not be as useful as in his own world, but he could learn to use magic to enhance his combat abilities. Also, he'd have to make new friends and enemies, and learn how to navigate the social politics of Hogwarts while still holding on to his own identity as a demigod.
Percy would be completely devastated. He might go into a state of shock at first, unable to believe that Annabeth is really gone. Then he could become filled with rage, vowing to take revenge on whoever or whatever was responsible for her death.
Maybe he faced an extremely powerful enemy that he couldn't overcome. It could be a new and terrifying monster created by the Titans or some other dark force.
Well, one possibility could be that Percy is framed for a crime he didn't commit. Maybe some powerful enemy uses magic or trickery to make it seem like he's violated a major demigod law. So, he's sent to a special prison for demigods. Inside, he has to deal with all sorts of other dangerous inmates, some of whom might be old enemies or just generally bad - tempered demigods. He'd probably try to find a way to prove his innocence and escape while also having to survive the various challenges within the prison.
In this fanfiction, perhaps Percy will make new friends at Goode who end up getting involved in his demigod world. There could be a plot where the school is in danger, and Percy has to use his powers and knowledge of the mythological world to protect it. Maybe he'll also have some interesting interactions with his teachers who suspect there's something different about him.
Perhaps in this fanfiction, Percy goes to Australia to find a hidden artifact that is crucial for the safety of the demigod world. Along the way, he teams up with local demigods (if there are any in the fan - created story). He would have to adapt to the Australian culture and environment, which is very different from what he's used to in the US. He might also face some new types of monsters that are native to Australia.