The interaction could also be more of a mentoring kind. Some of the Avengers, like Hawkeye, could teach the bird family members archery skills if they are intelligent enough. In return, the bird family could teach the Avengers how to better navigate through the air currents.
Tony could use his technology to analyze the popularity trends in Yelena fanfiction. He might say 'I can see which scenarios are the most popular in these fanfics about Yelena.' Natasha might take some of the positive portrayals in the fanfiction as a compliment to her sister. She could say 'This shows that Yelena is making an impact.' Thor might not fully understand but he could share the fanfiction stories in Asgard as a strange but interesting Midgardian thing.
Snape would probably start off being rather aloof. He'd observe the Avengers' behavior and abilities before making any real moves to interact. He could be sarcastic towards them, especially if they make assumptions about him or his magic. But as time goes on, he might start to see their value and open up a bit more, sharing some of his magical knowledge.
Naruto would interact in a very enthusiastic way. He'd be in awe of the Avengers' powers and would want to learn from them. At the same time, he'd show off his own ninja abilities. He might bond with Hulk over their shared 'rage' - like Naruto has his nine - tailed fox anger and Hulk has his own. He'd also try to cheer up the more serious Avengers like Black Widow with his positive attitude. And he'd probably try to get them all to do some ninja training together.
They might start by comparing powers. Superman's super strength and flight would be quite a topic. Thor would likely want to have a friendly competition with Superman in terms of strength. Then they could move on to sharing their experiences. Captain America could talk about his battles during World War II, and Superman could share his adventures in saving Metropolis. They could also team up to fight a new, powerful villain that neither could defeat alone. For example, a villain with the ability to nullify Superman's powers and hack into the Avengers' technology.
Supergirl would probably start by introducing herself and her powers. The Avengers would likely be in awe of her abilities. They might ask her to join them on a mission right away. Supergirl could say yes and then start showing off her skills during the mission.
In fanfiction, Venom could interact with the Avengers in many ways. For example, he might initially be seen as a threat and the Avengers try to subdue him. But then they could discover that he has some common enemies, like certain powerful villains who are a menace to both him and the Avengers. So, they could form an uneasy alliance.
The Avengers and the Eternals could interact in a variety of ways. The Hulk might be intrigued by Gilgamesh's strength. Black Widow could try to figure out the Eternals' motives. And on the Eternals' side, Sersi might befriend Scarlet Witch and learn about her magic. There could also be some friendly competitions between the two groups, like a race between Quicksilver and Makkari.
They can interact through battles. For instance, Naruto might face off against Thor in a friendly spar. Naruto's speed and agility could be pitted against Thor's strength and lightning powers.
The characters could interact through a shared mission. For instance, if there's a threat that endangers both the wizarding world and the world of the Avengers, they would have to work together. Harry could use his knowledge of magic to assist the Avengers in understanding the more mystical aspects of the threat, while the Avengers could use their combat skills and technology to fight the more physical parts of the enemy.
They might be in awe of each other at first. The Fanon Avengers could look up to the Canon Avengers as the originals, while the Canon Avengers might be intrigued by the unique takes on their characters in the Fanon world. They could start by comparing their powers and sharing stories about their adventures.