In many such fanfics, the Avengers might find Loki through various means. Sometimes it could be intelligence they gather about the location where he is being tortured. For example, they might intercept a message from Loki's captors or notice some strange energy signatures that lead them to the place.
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.
Future Loki might interact with the Avengers in a cautious way. He knows their past opinions of him and tries to prove himself. He could start by sharing small bits of useful information. For example, he might tell Iron Man about a weakness in a new enemy's technology.
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.
In this fanfiction, Loki might interact most with Hulk. It would be an interesting dynamic as Loki is a master of manipulation and Hulk is, well, the Hulk. Loki could either try to use Hulk for his own purposes, which would be very dangerous, or he could end up on the wrong side of Hulk's anger. But at the same time, it could also lead to some unexpected moments of understanding or at least a begrudging respect between them.
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.
One challenge could be the security around Loki. His captors might have strong defenses and guards. The Avengers would have to fight their way through to reach Loki.
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'.