This is post-Avengers fic. Loki is defeated and somehow ended up having his magic taken by Odin, though not the glamour. Deemed no longer dangerous, Odin cast him out of Asgard and somehow he ended up in Avengers Tower (Thor I think, because there are issues with Thanos? The only safe place for magicless Loki is the Tower). With no magic, Loki soon fall into depression with healthy dose of PTSD due to Chitauri torture, Odin A++ parenting and basically living with the enemy.
In the end, Loki helped all the Avengers battling enemy with robot-mutant thingies using his Jotun heritage (He's blue, armed with ice shards and basically proving to everyone that even with no magic he's still a BAMF) and almost died due to blood loss. He hurts his feet, and get stabbed in the lungs I think. Bruce lost him twice in the elevator.
The chapters are broken by each interaction with every Avengers and how they deal with him being there. Jarvis is naturally, become the first 'person' he's okay with. I remember Thor gave him a calender, Bruce left him with tea bags and thermos full of hot water because the only things he eats are toast and fruits (and lots lots of tea). The Avengers didn't warmed up to him easily though, only by increment. And Loki tends to stay away from them too, even if they lives on the same house.
Its not in AO3 or FFn though; I read it in LJ and kinkmeme (for the love of everything, I didn't remember what kinkmeme is that...) though perhaps the author has posted it elsewhere since then....
Any kind of help is appreciated!