Percy would probably grow in his leadership skills. Odin is often seen as a very strategic and powerful leader in Norse mythology. Under his influence, Percy could learn new ways to lead in battles and make decisions. He might also become more of a diplomat, trying to bridge the gap between the Greek and Norse worlds. For example, he could try to make alliances between Camp Half - Blood and the Norse heroes or gods. This would require him to be more diplomatic and understanding of different cultures.
Well, it could be a story full of epic adventures. Percy's demigod powers combined with Odin's influence might lead to him facing new and more powerful foes. He could be trained in different ways than he was in the original Percy Jackson series, learning skills more in line with Norse mythology.
At first, Percy would probably be angry and frustrated. Losing an eye is a huge deal. But he's also a determined person. He would start to practice with his remaining senses more intensively. He'd learn to listen more carefully for approaching enemies, feel the vibrations in the ground or water more acutely. He might also seek out some magical or medical help within the demigod world. There could be potions or spells that might help him either regain some vision or enhance his other senses to make up for the loss.
One possibility could be that Percy, being the banished son of Odin, has to prove himself in the world of Percy Jackson. Maybe he has powers from Odin that are not fully understood in the demigod world. He could go on a journey to discover his true identity and find a way to regain his place. For example, he might face challenges from both the Norse and Greek mythological beings. He may have to use his wits and newfound powers to overcome these obstacles.
Odin's loss of his eye was a significant act. He did it to gain profound wisdom and insights. This sacrifice was part of his journey to become a more powerful and knowing deity.
His powers would likely be a blend of his original demigod abilities and those of Odin. He may still retain some connection to water, but it could be transformed. Maybe he can turn water into ice like the Norse frost giants. Also, he could have Odin's gift of knowledge, which means he could understand ancient languages or know things about the past and future without being taught. This would give him an edge in battles and quests compared to the original Percy.
Well, different comics have different takes on it. But often, it's depicted as a powerful act of self-sacrifice to obtain some sort of divine knowledge or power.
In a Naruto Gets Odin's Eye fanfiction, there could be a plot where Naruto's world is somehow merged with the world of Norse mythology. The acquisition of Odin's eye could be a key factor in this merge. Naruto could use the eye to communicate with the Norse gods and gain their support in battles against his foes. This could also introduce new villains from Norse mythology. His friends in Konoha would be both amazed and a bit intimidated by his new power. Naruto would have to learn to control the power of Odin's eye quickly to prevent it from causing chaos in his village.
It's possible that his powers could even be enhanced in some ways. Losing an eye could make him more in tune with his other senses, and this could translate to his powers. For instance, his ability to sense danger through water vibrations could become sharper as he has to rely more on it. His powers might also develop in new directions. Maybe he could start to use water to create illusions to compensate for his lost vision in battle, like using water to project false images of himself to confuse his enemies.