Fun theme! I just have a few to add:
No Aphrodisiac by The WhitlamsAn odd letter, but a letter nonetheless.
Chain Letter by The BillysAh the curse of the chain letter, back when folks shared these banes via snail mail.
Letter from Belgium by The Mountain GoatsI'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!