In informal, ungrammatical but native AE, one can hear "Me and her" or
"Her and me" * as the subject (e.g., "Her and me went home.").  On the
other hand, "Me" or "Her" as the exclusive subject is apparently
"impossible" for the native AE speaker.  Why is this so?  What is the
difference between a single pronoun and two?  What about "Me or
her"?   It also seems to be possible.

*Also "Me and she"  and maybe "She and me"