Thor could also be someone Harry interacts with. Thor, coming from a mythical realm himself, might be more open to the idea of magic and could even share some of his Asgardian knowledge with Harry in return for learning about wizard magic.
He could interact with Iron Man. Iron Man would be curious about Harry's magic and might try to incorporate it into his tech somehow.
Maybe Harry could use some of his magic skills to assist the Avengers in a battle against a powerful enemy. For example, he could use a spell to freeze the bad guys momentarily while the Avengers strike.
Another character he could interact with is Thor. Thor's otherworldly nature and his powerful abilities would be quite a contrast to Stiles. Maybe Stiles could help Thor understand some earthly concepts while Thor could teach Stiles about Asgardian culture and power.
Maybe Thanos somehow discovers the wizarding world and decides he wants to add the power of magic to his collection of Infinity Stones. He could be the main villain, and Harry, with his understanding of both magic and his new Avengers - like abilities, would have to lead the fight against Thanos to protect both worlds.
It could be that Harry discovers he has some sort of connection to the Infinity Stones. So, the Avengers seek his help to understand and control the power of the Stones. Along the way, he has to deal with his own past traumas as well as the new threats in the Marvel world. He might teach the Avengers some magic too, like how to apparate short distances for quick escapes or attacks.
He could interact with characters from the crossover world who are used to the concept of motherhood. For example, if it's a crossover with a fairytale world, he might interact with fairy godmothers who could offer him advice on how to be a good mother.
Obviously, Buffy would be a major character he'd interact with. They could start off as wary of each other but then grow to respect one another's fighting skills. Giles too, as he has a wealth of knowledge about the supernatural, and he and Harry could have some interesting discussions about different types of magic.
The plot could involve Harry Potter being transported to the Avengers' universe. He might use his magic to help the Avengers fight against a common enemy, like Thanos. For example, his invisibility cloak could be used for stealth missions, and his spells could be a new form of defense against alien threats.
Well, perhaps Harry discovers the Avengers through some magical means like a spell gone wrong that transports him to the MCU world. He could be in awe of their powers and decide to learn from them, and then try to incorporate their fighting styles into his own magical battles.
One character could be Dobby. Even though Harry is living alone, Dobby might still find a way to visit him and offer his help. Another could be the Hogwarts ghosts. They can pass through walls and might visit Harry in his solitary abode.
Obviously, Hagrid could be one. He would be so amazed and probably take baby Harry on little adventures around the Hogwarts grounds, listening intently to what Harry has to say.