A lot vs. Alot: 9 Grammatical Pitfalls
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 (1938) is from the notion of speaking from notes written in haste on one's shirt cuffs. Off the rack (adj.) is from 1963; off the record 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.
"to kill," 1930, from off (adv.). Earlier verbal senses were "to defer" (1640s), "to move off" (1882). Related: Offed.