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.
c. 1300, "shield," diminutive of late Old English targe, from Old French targe "light shield" (12c.), from Frankish *targa "shield," from Proto-Germanic *targ- (source also of Old High German zarga "edging, border," German zarge "border, edge, frame," Old English targe, Old Norse targa "shield, buckler"), perhaps originally "edge of a shield." Meaning "round object to be aimed at in shooting" first recorded 1757, originally in archery, perhaps suggested by the concentric circles in both. Target-practice is from 1801. Target audience is by 1951; early reference is to Cold War psychological warfare.