I've read literally hundreds of Loki stories, and will read all kinds of tropes I can think of some stories which fill part of your request, though a lot of what I read is Thorki. Are you OK with frostiron or other slash Loki pairings? I do read het and gen as well.
Here’s one of my all-time favorite stories. It deals with issues of racism and internalized racism, and what defines the word “monster”. There’s some great conversations with Loki and Bruce. There’s a good scene when clueless but good bro Thor tries to tell the rest of the Avengers about a quest when Loki saved the day, but still manages to mostly leave that part out. There’s another scene in which Thor admits, if he’d been sent to Midgard with his powers intact, he might have tried to conquer it as well. I have so many favorite scenes in this story it’s hard to just choose a couple. I hope it fits your request, at least a little bit.
Ask Me No Questions by Alex51324 When Thor returns from Asgard to rejoin the Avengers, he brings Loki in tow--stripped of his magic and bound with a geas that allows him to speak only in response to direct questions. AKA, yet another "Loki lives with the Avengers; chaos ensues" story. http://archiveofourown.org/works/887344
You said "Fics where Odin didn't bring home a changeling child simply to use him to further his own kingdom, but rather because he couldn't let a baby die of exposure."
Here's a short piece which fits that description:
A Holy Place by Rynfinity http://archiveofourown.org/works/3188678
And - I know this is the complete opposite of what you requested but this is an excellent redemption story and it's one of the few where Odin doesn't punish Loki but gets him the help he needs to recover. Plus, it has a great plot.
Overlapping Spaces by khilari, Persephone_Kore Summary: Thor returns to Earth a month after the Chitauri invasion to keep his promises -- to see Jane again, and take her to see Asgard, even if the rainbow bridge is still undergoing repairs. Not that Jane is complaining about watching the repairs. But she wasn't expecting Loki to be haunting the palace library, even in psychiatric care; and Loki wasn't expecting to make friends with Thor's mortal girlfriend. http://archiveofourown.org/works/591735/chapters/1065162
I'll try to think of a few more non-slash stories which fit your request.
no subject
Here’s one of my all-time favorite stories. It deals with issues of racism and internalized racism, and what defines the word “monster”. There’s some great conversations with Loki and Bruce. There’s a good scene when clueless but good bro Thor tries to tell the rest of the Avengers about a quest when Loki saved the day, but still manages to mostly leave that part out. There’s another scene in which Thor admits, if he’d been sent to Midgard with his powers intact, he might have tried to conquer it as well. I have so many favorite scenes in this story it’s hard to just choose a couple. I hope it fits your request, at least a little bit.
Ask Me No Questions by Alex51324
When Thor returns from Asgard to rejoin the Avengers, he brings Loki in tow--stripped of his magic and bound with a geas that allows him to speak only in response to direct questions. AKA, yet another "Loki lives with the Avengers; chaos ensues" story.
http://archiveofourown.org/works/887344
You said "Fics where Odin didn't bring home a changeling child simply to use him to further his own kingdom, but rather because he couldn't let a baby die of exposure."
Here's a short piece which fits that description:
A Holy Place by Rynfinity
http://archiveofourown.org/works/3188678
And - I know this is the complete opposite of what you requested but this is an excellent redemption story and it's one of the few where Odin doesn't punish Loki but gets him the help he needs to recover. Plus, it has a great plot.
Overlapping Spaces by khilari, Persephone_Kore
Summary: Thor returns to Earth a month after the Chitauri invasion to keep his promises -- to see Jane again, and take her to see Asgard, even if the rainbow bridge is still undergoing repairs. Not that Jane is complaining about watching the repairs. But she wasn't expecting Loki to be haunting the palace library, even in psychiatric care; and Loki wasn't expecting to make friends with Thor's mortal girlfriend.
http://archiveofourown.org/works/591735/chapters/1065162
I'll try to think of a few more non-slash stories which fit your request.