A possible start could be a prophecy in both the wizarding world and Asgard. The prophecy foretells of a great danger that can only be averted if a wizard from Hogwarts and a warrior from Asgard join forces. Harry Potter and Thor are then made aware of this prophecy and set out on a journey to find each other and figure out how to stop the impending doom.
The plot would change a great deal. For one, Harry would be much more powerful physically. So when facing Voldemort, he could use Thor's strength in combat, not just rely on magic. He might be able to take on Death Eaters more easily.
Well, Thor is a very confident and powerful character. He might be initially a bit baffled by the wizards and witches at Hogwarts. Harry, on the other hand, would be in awe of Thor's strength and abilities. Thor could probably teach Harry some physical combat skills, while Harry could introduce Thor to the subtleties of wizard magic like apparition.
It could start with a magical accident in the Harry Potter world. For example, a spell gone wrong during a Hogwarts class creates a portal that sucks Harry into the world of One Piece, right onto Whitebeard's ship. The crew is initially suspicious but Whitebeard, sensing something different about Harry, decides to let him stay for a while.
Well, in a fanfiction where Harry Potter meets Thor, there could be a really interesting exchange of magic and godly powers. Harry might be in awe of Thor's thunder - based abilities, while Thor could be intrigued by the complex magic of the wizarding world. Maybe they'd team up to fight some dark force that threatens both their realms.
He might become more bold. Thor is a very bold character, and his influence could make Harry less hesitant.
Well, Harry Potter would probably become an even more powerful wizard. Thor's combat skills and physical strength could be incorporated into Harry's magical abilities. Maybe he'd be able to cast spells while doing some of Thor's epic leaps and strikes.
The fanfiction could start with Poison Ivy being magically transported to the wizarding world. She finds herself in the Forbidden Forest and starts to spread her influence among the native plants there. Harry Potter, while on a patrol in the forest, notices the strange changes in the plants and is the first to encounter Poison Ivy, leading to a tense first meeting between the two.
It could start with Harry having a strange dream about a cold, snowy land filled with direwolves. He wakes up curious and through some magical accident, ends up in the world where Brandon Stark lives. This sudden appearance in a new world full of different rules and politics would be the starting point of their adventure together.
Well, if Harry Potter was raised by Thor, his character would likely be more bold and fearless. Thor's warrior - like nature would rub off on Harry. He might be more upfront in facing challenges instead of being a bit hesitant as he sometimes was in the original series. Harry would probably have a different view on magic too, seeing it more as a powerful tool like Thor views his hammer, rather than just a means to an end in the wizarding world.
His powers could work in a really interesting way. Since Thor is associated with lightning, he might be able to cast spells related to electricity in a much more powerful way than normal wizards. For example, he could create bolts of lightning as offensive spells. His demigod strength could also come in handy, like being able to break through magical barriers that would be difficult for regular wizards to overcome.