In 1855 a European goat farmer by the name of Hoek Hogan raised a particularlydisgusting goat. This goat quickly became famous for being the most horrific smelling and ugly creature to wander the fields. It is legend that his scent could be detected from over a kilometer away (.6217 miles).
To compare something to hogan's goat is considered a great insult.
"Timmy hasn't bathed in a week. He smells like Hogan's goat"
"She wanted me to eat her pussy, but it looked like Hogan's goat. So I ate out her butt instead"
Hogan's Goat is a 1965 play by William Alfred. (Wiki). The common phrase is "This makes Hogan's Goat look like a precision instrument!" It is less about being 'totally f*****d' and more a ludicrous, convoluted lampoon of politics in general.