Thor would be a likely candidate. Since he is Loki's brother, he already has a connection with him. Thor might be the one to convince the other Avengers to give Loki a chance and be the first to reach out and try to befriend him in this new situation.
There's a fanfic called 'The Loki - Avenger Alliance'. In this story, Loki is forced to team up with the Avengers due to a common threat from another dimension. It's full of action scenes and interesting dialogues between the characters, especially Loki's sarcastic remarks which are really in - character.
He would probably interact a lot with Thor. Since they are brothers, there is a pre - existing relationship full of complexity. Also, he might interact with Iron Man quite often. Tony Stark's sarcastic nature and Loki's trickery could lead to some really interesting exchanges, either in the form of verbal sparring or working together on some high - tech and magic - combined projects.
If Loki impersonated Thor, the real Thor would be furious when he found out. The other Avengers, like Iron Man, might initially be confused but then quickly realize something is off. Iron Man would likely use his technology to detect the impostor. Hulk might just smash first and ask questions later when he senses something wrong with 'Thor'.
One common theme is redemption. Since Loki has done a lot of bad things in the original stories, many fanfics focus on him trying to make up for his past actions and gain the trust of the Avengers. Another theme is family, especially his relationship with Thor which often plays a big part in the stories. Power is also a theme, like how Loki's magic can be both a threat and an asset to the Avengers.
One idea could be that Loki gets turned into a vampire while in the midst of his schemes against the Avengers. This new state gives him different powers and motives. He might struggle with his newfound thirst and also use his vampire abilities to outwit the Avengers in different ways.
In a Truth or Dare Avengers and Loki fanfic, there could be a really funny scene where Loki is dared to transform into Captain America and do his patriotic speech in a comical way. It would be hilarious to see Loki's take on Steve Rogers' serious moments.
One interesting Loki and Avengers fanfiction could be where Loki is forced to team up with the Avengers against a greater threat. Maybe an ancient evil that even Loki realizes is too dangerous to face alone. He grudgingly works with them, and along the way, there are lots of humorous exchanges as the Avengers don't trust him at first.