Fun theme! I just have a few to add:
No Aphrodisiac by The Whitlams
An odd letter, but a letter nonetheless.
Chain Letter by The Billys
Ah the curse of the chain letter, back when folks shared these banes via snail mail.
Letter from Belgium by The Mountain Goats
I'm including this mostly because I just watched Band of Brothers and am kinda thinking of this letter being during that time, although it's not. It also has one of the weirdest lyrics, "That's good, we can always use some more electrical equipment."
Mother Mother by Tracy Bonham
Okay, technically a phone call rather than a letter, but sounds like a letter to me. The kind of letter a parent dreads!