If Percy Jackson goes to Alagaesia in fanfiction, he'd likely meet Murtagh. Their first meeting might be a bit tense as Murtagh has his own complex story. Percy might also encounter Nasuada, the leader of the Varden. She would be intrigued by Percy's powers and his origin. And there's a good chance he'd meet Galbatorix as well, which would be a very dangerous encounter considering Galbatorix's power.
Percy could meet Saphira, the dragon. Given Percy's curious nature, he'd be both amazed and a bit cautious around such a magnificent and powerful creature. Also, he might come across Arya, a strong and intelligent elf. Their meeting could lead to exchanges of knowledge, with Percy sharing about his world and Arya about hers.
He would probably meet Eragon. Eragon is a key figure in Alagaesia, and their encounter would be full of surprises as they come from different worlds with different powers.
Well, he might get into all sorts of adventures. He could meet the dragons in Alagaesia and try to use his water powers to his advantage against them. Maybe he'd team up with the local heroes there and learn new combat styles.
He could meet some Aboriginal heroes or spirits. They might have their own powers and knowledge that Percy can learn from.
Percy might meet an old enemy who has somehow been resurrected or changed in the future. This enemy could be more powerful and have a new plan to take over the world or destroy the demigods. Or he could meet a group of time - traveling demigods from an even further future who are trying to fix something in Percy's future that has gone wrong.
Percy might run into Loki. Loki is known for his trickery. He could either befriend Percy for his own devious plans or try to deceive him. Percy, being used to dealing with tricky situations in his own world, would have to be on his guard against Loki's schemes.
The plot might involve Percy getting lost in Alagaesia. He then has to figure out how to get back home while also getting involved in the local politics and power struggles. Since he's a demigod, he might be seen as a powerful ally or a threat. He could end up using his knowledge of Greek mythology and his own powers to outwit the various factions in Alagaesia.
Eragon could be one of Percy's allies. Eragon has his own set of powers and knowledge of Alagaesia. Percy and Eragon could combine their skills, with Percy's control over water and Eragon's magic and sword - fighting abilities. They could also share their different cultural knowledge, Percy from the world of Greek mythology and Eragon from the world of Alagaesia.
Well, one possible plot could be Percy using his water - controlling abilities in the world of Alagaesia. Maybe he teams up with the local heroes there and they face some common enemy. For example, a powerful dragon that is threatening both the demigods' world and Alagaesia. He could also introduce new combat styles to the people of Alagaesia based on his training at Camp Half - Blood.
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.
He might meet a new teacher who is secretly a minor god or goddess in disguise.
It could be an ancient and powerful dragon that has been awakened by the arrival of Percy in Alagaesia. The dragon might see Percy as a threat to its rule or territory and decides to go after him. This dragon could also have some special abilities that make it difficult for Percy to defeat, like being able to nullify his water powers for a short time.