Another possibility is a story where a spell goes wrong in the Harry Potter world and opens a portal to Asgard. Harry and his friends end up in Asgard and meet Lady Sif. They form an alliance to stop an evil wizard who has also found his way to Asgard and is trying to steal Asgardian magic for his own dark purposes. Lady Sif could teach them some Asgardian magic while they introduce her to things like the Marauder's Map.
Yes, there are some out there. You can start by looking on fanfiction websites like Archive of Our Own. Just search for 'Harry Potter and Lady Sif' and you'll likely find a variety of stories, some might be about them teaming up in a magical adventure, or perhaps a crossover story where the worlds of Harry Potter and Thor (where Lady Sif is from) collide in an interesting way.
One idea could be a crossover where Naruto is somehow transported to the realm where Lady Sif is from. They could team up to fight a common enemy. Naruto's unique jutsu and Lady Sif's combat skills would make for an interesting combination.
Well, a frequent theme is adventure. They often embark on some grand adventure together. Maybe it's to save both their worlds from a great threat. Also, the theme of mutual understanding. Given their different upbringings and worlds, the stories often focus on how they come to understand and respect each other. And sometimes there's a theme of discovery, like Harry discovering new things about Asgard or Lady Sif learning about the wizarding world.
Another concept could be that Harry Potter discovers he has a connection to Magneto's mutant powers. This might happen during a strange encounter with a dark magic object that unlocks a latent power within him. He then has to learn how to control these new abilities while also dealing with the threats in his own wizarding world, and he might seek out Magneto for guidance in a secret meeting across the boundaries of their two worlds.
One idea could be that Hawkgirl somehow gets transported to the Harry Potter universe. Maybe she arrives during a Quidditch match and her flying skills astound everyone. She could then join forces with Harry and his friends to fight against the dark forces in Hogwarts, using her Nth metal mace and flight abilities in unique ways.
One idea could be a crossover where Harry Potter accidentally ends up in the world of Ranma 1/2. Maybe he's on a magical experiment gone wrong and lands in Nerima. He could use his magic to help Ranma deal with his curse, like creating a spell to keep him from changing into a girl when splashed with cold water.
One idea could be a crossover where Harry Potter accidentally travels to the One Piece world and meets Whitebeard. He could learn about their different forms of magic and power, and together they face a new threat that combines the dark magic from his world and the powerful pirates in the One Piece world.
One idea could be that Fluttershy somehow gets transported into the Harry Potter world. Maybe she arrives at Hogwarts as a new kind of magical creature that the students have never seen before. Her gentle nature might initially cause confusion among the more rowdy students, but she could gradually make friends with the likes of Luna Lovegood, who would be intrigued by her uniqueness.
One idea could be that Gandalf somehow gets transported to the Harry Potter universe. He could become a mentor to Harry, using his vast magical knowledge and wisdom from Middle - earth. Maybe he helps Harry understand some ancient magic that even Dumbledore wasn't fully aware of.
One idea could be a crossover where Kakashi is summoned to the Harry Potter world by a dark magic spell gone wrong. He then uses his ninja skills and Sharingan to navigate the wizarding world, perhaps even teaching some Defense Against the Dark Arts classes with his unique combat knowledge.