He might also get involved in some sort of epic quest. The Greek Gods are known for setting heroes on grand adventures. Harry could be sent to retrieve a powerful magical artifact that has been lost for centuries, with the help or hindrance of the Gods. It could be a race against time as some dark force also wants the artifact.
It could be that the gods view Harry as a novelty at first. They might be amused by his wizarding skills. However, as time goes on, they could see his potential and offer him a place among them. But Harry, being loyal to his friends and the wizarding world, would be hesitant. He would have to decide whether to embrace this new life with the gods or stay true to his roots. This internal struggle could be a major part of the fanfiction.
In this 'batman meets greek gods fanfiction', perhaps Batman teams up with a Greek god. For example, he could join forces with Athena. She is the goddess of wisdom, and she might help Batman come up with new strategies to fight his enemies in Gotham. Batman, in return, could show her the modern ways of combat and detective work.
The Greek gods would likely have a range of reactions. Poseidon might be interested in the use of water in the magical world, like the Black Lake at Hogwarts. Hermes could be fascinated by the idea of owls delivering mail instead of his usual role as a messenger. Some gods might dismiss it as a mere mortal's wild imagination, while others could see it as a new form of creative storytelling that has its own allure.
Well, it could be that the Greek gods see Harry as a special being. They raise him on Mount Olympus. He would be taught by Athena in wisdom, so he'd be not only a powerful wizard but also extremely intelligent. His upbringing among the gods would give him a different perspective on good and evil. When he returns to the wizarding world, he'd use the values and powers he gained from the Greek gods to fight Voldemort. Maybe he'd use the gift of prophecy from Apollo to foresee Voldemort's moves.
In such a fanfiction, perhaps Harry Potter could use magic to communicate with the aliens. For example, he might use a spell to translate their strange languages.
Well, it could be that the Queen, being a symbol of order in the Muggle world, has to deal with the sudden appearance of Harry Potter and the chaos that magic can bring. Maybe she initially mistakes his magic for some sort of advanced technology and there are a series of misunderstandings that lead to an interesting adventure. Harry could introduce her to the concept of Hogwarts and she might be fascinated by the idea of a school for magic.
Well, one possibility is that the magic from the Harry Potter world and the chakra-based abilities in Naruto could combine in interesting ways. For example, a wizard might learn to use chakra to enhance their magic spells, or a ninja could use a magic spell to give them an edge in combat. Another idea could be that the characters from both universes team up to fight a common enemy. Maybe Harry Potter and Naruto could join forces to defeat a powerful dark wizard or a rogue ninja.
Well, it could be that God appears to Harry in a moment of great despair. He might show Harry the true nature of life and death in the wizarding world. Harry could learn about the deeper meaning behind the magic he wields and how it is all part of a greater plan designed by God. God could also guide Harry on how to use his powers more morally and justly, not just for the sake of defeating the Dark Lord but also for the betterment of the entire wizarding community.
Well, perhaps Harry Potter could use his magic against Shendu's dark powers. For example, he might try to counter Shendu's spells with his own powerful incantations like Expelliarmus. It would be an epic battle of magic from two different fictional universes.
One possibility is that Medusa is somehow brought into the Hogwarts grounds. This would cause chaos among the students and teachers. Harry, being the hero he is, would step up. He might research ancient spells and potions to deal with Medusa. He could also enlist the help of his friends like Hermione, who would dig into the library to find any information about Medusa in the wizarding world's history, and Ron, who would be there for moral support and also to help in any practical ways they could come up with.