"unawares," by 1936, American English, from off (adv.) + base (n.); a figurative extension from baseball sense of a runner being "not in the right position" (1882) and vulnerable to being picked off.

also offhand, 1690s, "at once, straightway," from off (prep.) + hand (n.). Probably originally in reference to shooting "from the hand," without a rest or support. Hence, of speech or action, "without deliberation, unpremeditated" (1719). Related: Off-handed; off-handedly.

"forbidden, outside the limits within which a particular group or person must remain," by 1881, U.S. military academies jargon, from off (prep.) + limit (n.). Earlier (1857) it was applied to cadets, etc., who were in violation of the limitations on their movement and behavior.

1926, of railroads, "not done on a railway;" 1950, in computing, "not controlled by or connected to a computer or network;" from off (prep.) + line (n.).

1848, "a period when business is down," from off- (adj.) (see off (prep.)) + season (n.).

"white with a tinge of gray or yellow;" as an adjective, "almost the same as white," 1927, from off (prep.) + white (n.).

as a modifier, attested by 1941. The expression is much older (1610s). Related: Do-it-yourselfer.

1858, "defective or inferior because not of a natural or proper color," from off (prep.) + color (n.); originally used of gems; figurative extension to "not of the proper character, of questionable taste, risqué" is American English, 1867.

by 1911, of music or singing, "not having the correct tone or pitch, out of tune," from off (prep.) + musical sense of key (n.1). Figurative sense "not in accordance with what is appropriate in the circumstances" is by 1943.