filth n.

Old English ful "rotten, unclean, vile, corrupt, offensive to the senses," from Proto-Germanic *fulaz (source also of Old Saxon and Old Frisian ful, Middle Dutch voul, Dutch vuil, Old High German fül, German faul, Gothic füls), from PIE *pu- (2) "to rot, decay," perhaps from the sound made in reaction to smelling something bad (see pus).

Old English ful occasionally meant "ugly" (as contrasted with fæger (adj.), modern fair (adj.)), and this sense became frequent in Middle English. The cognate in Swedish is the usual word for "ugly." Of weather from mid-14c. In the sporting sense of "irregular, unfair, contrary to established rule or practice" it is first attested 1797, though foul play is recorded from mid-15c. Baseball sense of "out of play" attested by 1860.

late 12c., fulthe, "corrupt, sinful," from filth + -y (2). Meaning "physically unclean, dirty, noisome" is from late 14c. Meaning "morally dirty, obscene" is from 1530s.

In early use often hardly more emphatic than the mod. dirty; it is now a violent expression of disgust, seldom employed in polite colloquial speech. [OED]

Related: Filthily; filthiness.

Middle English shit "diarrhea," from Old English scitte "purging, diarrhea," from source of shit (v.). The general sense of "excrement" dates from 1580s (Old English had scytel, Middle English shitel for "dung, excrement;" the usual 14c. noun for natural discharges of the bodies of men or beasts seems to have been turd or filth). As an exclamation attested in print by 1920 but certainly older. Use for "obnoxious person" is by 1508; meaning "misfortune, trouble" is attested from 1937.

Shit-faced "drunk" is 1960s student slang; shit list is from 1942. Shit-hole is by 1937 as "rectum," by 1969 in reference to undesirable locations. Shitload (also shit-load) for "a great many" is by 1970. Shitticism is Robert Frost's word for scatological writing.  

Up shit creek "in trouble" is by 1868 in a South Carolina context (compare the metaphoric salt river, of which it perhaps a coarse variant). Slang not give a shit "not care" is by 1922. Pessimistic expression same shit different day is attested by 1989. To get (one's) shit together "manage ones affairs" is by 1969. Emphatic shit out of luck is by 1942.

The expression when the shit hits the fan "alluding to a moment of crisis or its disastrous consequences" [OED] is attested by 1967.

The expression is related to, and may well derive from, an old joke. A man in a crowded bar needed to defecate but couldn't find a bathroom, so he went upstairs and used a hole in the floor. Returning, he found everyone had gone except the bartender, who was cowering behind the bar. When the man asked what had happened, the bartender replied, 'Where were you when the shit hit the fan?' [Hugh Rawson, "Wicked Words," 1989]