You might be feeling rather stupid the morning after with a hangover, but you don't have to talk like an idiot!

The term's etymology shouldn't be too hard to figure out: it's derived from the action of hanging over the damn toilet in the morning. Here's a few lesser-known synonyms and colloquialisms for hangover:

-Babbelas (South African slang)
-Veisalgia (Medical)
-Overhung (English Slang)
-Greek Flu (English slang)
-Two-Day Terry (Australian, describing a 2-day hangover, named in honor of Terry Wogan)
-Bleary Eyed (Australian slang)
-A Bit Gone English/Australian slang

Sources:
http://www.geocities.com/NapaValley/4699/slang-atoe.htm
http://www.hairytongue.com
& various websites