Perhaps a new character, a hybrid of a dark wizard and a Frost Giant. This being could be created by a dark ritual that combines the cold magic of the Frost Giants with the dark arts of the wizarding world. He would be after the power of both Thor and Harry, aiming to create a new realm where he is the sole ruler, using the powers of both Asgard and the wizarding world to his advantage.
A powerful dark wizard who has somehow managed to tap into Asgardian magic could be the main antagonist. He might have found an ancient artifact that gives him access to Thor's powers but twists them into something dark. He wants to rule both the wizarding world and Asgard, and sees Harry and Thor as the biggest threats to his plans.
It could be Loki. Since he has a knack for causing trouble, he might find a way to cross over to the wizarding world. He could manipulate the dark wizards and use their magic for his own devious plans. Maybe he wants to steal the Philosopher's Stone to gain immortality and use it to take over Asgard as well.
One possible plot could be that Thor ends up in the wizarding world of Harry Potter. Maybe the Bifrost malfunctions and he lands near Hogwarts. He could be mistaken for a very powerful wizard at first. Then he teams up with Harry Potter and his friends to fight against a new dark threat that is using both magic and some form of Asgardian - like power. Thor could teach the wizards about Asgardian combat and they could teach him more about the nuances of magic.
A powerful dementor - like being that has been corrupted by Asgardian dark magic. This entity could be draining the life force of both wizards and Asgardians. It would be up to Thor and Harry Potter to find a way to stop it, as it poses a threat to both of their worlds.
It could be Voldemort. Since he is the main bad guy in the Harry Potter series, it would make sense for him to be the antagonist. He might see the daughter of Thor as a threat to his plans of taking over the wizarding world.
One common theme is the clash of cultures. Harry comes from a world of wizards with their own set of rules and traditions, and Thor is from Asgard with its warrior culture. Another theme could be the exploration of power. Harry has his magic, and Thor has his godly strength. Writers often like to see how these two forms of power interact.
Yes, there are quite a few out there. You can start by looking on fanfiction websites like Archive of Our Own. Just search for 'Harry Potter x Thor Odinson' and you'll get a list of stories. Some might be crossovers where Harry and Thor meet in a magical world, while others could have more creative plotlines like Thor visiting Hogwarts or Harry traveling to Asgard.
There could be a new character created specifically for the fanfic. A dark wizard who has been observing the wizarding world from the shadows and sees Hisoka's arrival as an opportunity. This new antagonist could try to use Hisoka to achieve his own evil goals, like opening a portal to a dark dimension or stealing all the magic in the world. When Hisoka realizes he's being used, he would turn against this new antagonist, and Harry Potter and his friends would join him in the fight.
It could be a powerful dark wizard who has somehow made his way into the Avengers' universe. Maybe a wizard who was banished from the wizarding world in Harry's universe and has now joined forces with some of the Avengers' villains.
It's really hard to say. Thor has superhuman strength and can control lightning. But Harry Potter has a whole arsenal of spells. If Harry could manage to disarm Thor quickly with Expelliarmus, he might have a chance. However, Thor's physical power is no joke. One swing of his hammer could cause a lot of damage.
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.
One possible plot could be that Thor somehow gets transported to the wizarding world. He might initially be confused by the magic there as it's different from his Asgardian powers. Harry Potter and his friends could be intrigued by Thor and his hammer. They might team up to fight a common enemy, perhaps a dark wizard who has somehow got hold of some Asgardian artifact and is misusing its power.