The story could develop from a misunderstanding. Sigyn is seen doing something strange on Earth, and the Avengers think she's up to no good. They try to stop her. But as they engage in a fight, they realize she's not as bad as they thought. Sigyn then explains her situation, perhaps she's looking for something that was lost on Earth. The Avengers offer to help her. Along the way, they encounter various enemies and Sigyn's unique powers and knowledge help them out. This leads to a deeper relationship between Sigyn and the Avengers as they continue their adventures together.
The story could start with a call for help. Maybe an enemy that the Agents of SHIELD can't handle alone is causing havoc. So they reach out to the Avengers. Then there would be a period of getting to know each other. Some characters might not trust each other at first. But as they face challenges together, like fighting a powerful super - villain, they start to bond.
In some fanfictions, Sigyn might be brought to Earth by accident and the Avengers initially mistake her for a threat. But as they get to know her, they realize she can be a great ally. For example, she could have the ability to heal some of the Avengers' wounds that normal medicine can't. And she might also introduce them to some Asgardian technology or magic that they can use in their future battles.
Some relationships might start off rocky. The Avengers have grown used to their independent lives, and the parents may come across as overbearing at first. But over time, they could learn to respect each other. For example, an Avenger might initially resist their parent's advice but later realize it was valuable.
Often, Loki is still portrayed as his complex self, full of trickery, but Sigyn can be the one to humanize him more in the Avengers fanfiction. For instance, she might show the other Avengers that there's more to Loki than just his villainous deeds.
The Avengers might react in different ways. Steve Rogers would probably be polite but firm in getting to know Peter's boyfriend. He'd want to ensure that he was a good influence on Peter. Thor, on the other hand, might be a bit more boisterous. He could either be really friendly and enthusiastic, or his loud and powerful presence might accidentally scare the boyfriend a bit.
In Avengers fanfiction, Loki and Sigyn can be depicted in various ways. One could have Sigyn as a force for Loki's redemption within the Avengers' universe. She might use her connection to Loki to try and sway him from his more villainous tendencies, adding an interesting dynamic to the Avengers' storylines.
Thor would likely have a very complex interaction. Since Hela is his sister, there would be a mix of family drama and conflict. The other Avengers might be initially distrustful of Hela. Iron Man could crack sarcastic remarks at her. Captain America would try to keep the peace and assess the situation. Hela, on her part, might look down on the Avengers at first, seeing them as lesser beings compared to her Asgardian power.
Thor would likely be the most affected. He has a history with Fenrir as it is from Asgardian mythology. He might be cautious at first, but also feel a sense of kinship. Iron Man would probably be all about analyzing Fenrir, trying to figure out its weaknesses and strengths. Captain America would be on guard, ready to defend his team, but also open to the idea of Fenrir not being an enemy if proven so.
The Avengers in quarantine fanfiction would show some interesting relationship developments. Maybe Rhodey would visit from time to time, bringing some outside perspective. This could cause some friction as the Avengers are used to their own little world during quarantine. But it could also be a source of new ideas. Sam and Bucky might continue their banter but also become closer as they train together within the quarantine area. And Pepper could play an important role in keeping Tony in check and also in mediating any disputes that might arise between the Avengers members.
Well, if the Avengers meet Peter's girlfriend, it depends on their own personalities and what they've heard about her. If they've heard good things from Peter, some like Spider - Man himself would be very excited to introduce her. The Avengers might be a bit cautious too, because they don't want any harm to come to Peter or their team because of her. For example, if she has a past that's a bit murky, they'll be on high alert. But if she's just a normal, nice girl, most of them would eventually warm up to her, except maybe those who are more cynical like Loki (if he was somehow part of the Avengers in this fanfiction), who would always be suspicious.