The most fucked up thing known to man (often said by older people) Something that is so screwed up it is not even understandable.

Intelligence agency term for "psychological operation". A government or corporate-sponsored operation, usually taking the form of a "terrorist attack" or "crazed gunman on a spree", with the intent of panicking the public into demanding more police and laws inhibiting freedom. Psyops are usually carried out by drugging a civilian or group of civilians with aggression-promoting drugs, psyching them up, arming them, and sending them out to commit mayhem. Government-sponsored terrorism. See also blackshirts, conspiracy

In 1855 a European goat farmer by the name of Hoek Hogan raised a particularly disgusting 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.

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.