by c. 1200 as an emphatic form of Old English of (see of), employed in the adverbial use of that word. The prepositional meaning "away from" and the adjectival sense of "farther" were not firmly fixed in this variant until 17c., but once they were they left the original of with the transferred and weakened senses of the word. Meaning "not working" is from 1861.

Off the cuff "extemporaneously, without preparation" (1938) is from the notion of speaking from notes written in haste on one's shirt cuffs. In reference to clothing, off the rack (adj.) "not tailored, not made to individual requirements, ready-made" is by 1963, on the notion of buying it from the rack of a clothing store; off the record "not to be publicly disclosed" is from 1933; off the wall "crazy" is 1968, probably from the notion of a lunatic "bouncing off the walls" or else in reference to carom shots in squash, handball, etc.

Old English æftan "from behind, behind, farthest back," superlative of Old English æf, af, of "away, away from, off" (from PIE root *apo- "off, away"). Cognate with Old Frisian eft "later, afterwards; as well," Old Norse eft "after," Middle Dutch echter, efter "later, again," Gothic afta "behind, past." The Germanic superlative suffix *-ta corresponds to PIE *-to (compare Greek prōtos "first," superlative of pro "before"). The word is now purely nautical, "in, near, or toward the stern of a ship."

1520s, originally a second crop of grass grown on the same land after the first had been harvested, from after + -math, from Old English mæð "a mowing, cutting of grass," from PIE root *me- (4) "to cut down grass or grain."

Also known as aftercrop (1560s), aftergrass (1680s), lattermath, fog (n.2). Figurative sense is by 1650s. Compare French regain "aftermath," from re- + Old French gain, gaain "grass which grows in mown meadows," from Frankish or some other Germanic source similar to Old High German weida "grass, pasture."

When the summer fields are mown,
When the birds are fledged and flown,
      And the dry leaves strew the path;
With the falling of the snow,
With the cawing of the crow,
Once again the fields we mow
      And gather in the aftermath.  

[Longfellow, from "Aftermath"]