Well, in the official Marvel universe, there's no indication that the Avengers sit around watching Thor fanfic. Fanfic is more of a thing for fans in our world, not something the characters themselves would engage with in the main storylines.
One popular trope is the 'revelation' trope. For example, the Avengers might watch Thor's past battles and learn something new about him that changes their perception. It could be a hidden strength or a past sacrifice.
You can try websites like Archive of Our Own (AO3). It has a large collection of fanfiction, and you can easily search for 'Avengers watch Thor' fanfiction there. Just type in the relevant keywords in the search bar, and it will show you a list of stories.
One great Thor and Avengers fanfiction is 'The Reunion'. It focuses on Thor's return to the Avengers after being away for a while. The story does a great job of showing his relationships with the other members, especially how he reconnects with Tony Stark after some previous tensions. It has some exciting battle scenes as well.
They might see events that shaped Loki into the mischievous and sometimes villainous character he is. For example, the discovery of his true heritage. This could make the Avengers more sympathetic towards Loki, or it could make them more cautious, seeing how his past traumas have influenced his actions. In fanfiction, there could be all sorts of creative interpretations of these past events that would surprise the Avengers.
There's a fanfic called 'Loki's Redemption in Thor's World'. This one focuses on Loki trying to find his place in Thor's world after all the chaos he has caused. It shows his struggle to be accepted and how Thor is gradually coming to terms with having Loki back in his life. The writing style is engaging and really makes you feel for both characters.
A popular one is 'Thor and Loki: Brothers United in Battle'. This fanfic focuses on the bond between Thor and Loki. It shows how they work together to face a new threat that is even greater than the ones they've faced before. The story has a lot of character development for both of them. Loki uses his cunning to outwit the enemy, while Thor uses his strength. It's a great read for those who love to see the dynamic between these two brothers within the Avengers universe.
Steve Rogers, on the other hand, would be a bit more diplomatic. He might not fully understand the concept of fanfiction at first, but he'd respect the creativity of the fans. He could say that while it's not the 'official' story, it shows how much people love Thor and the Avengers. He might even find some of the stories that highlight Thor's heroic side inspiring for his own leadership.
One great fanfiction could be 'The Avengers' Reaction to Thor: The Dark World' where the Avengers watch the movie together and their hilarious reactions are described. It's a fun read that plays on the different personalities in the team.
You can try Archive of Our Own (AO3). It has a large collection of fanfictions on various topics, including this one. Just use the search function and type in 'Avengers watch Thor 2' and you'll likely find many interesting stories. Another option is Fanfiction.net. It also has a wide range of fan - created content, although the interface might be a bit more dated compared to AO3.