Etymology
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off-line (adj.)

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.).

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off-season (n.)

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

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off-white (n.)

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

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off-color (adj.)

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.

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off-key (adv.)

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.

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back off (v.)
"retreat, stop annoying someone," by 1938, from the verbal phrase, from back (v.) + off (adv.).
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cut-off (n.)

also cutoff, 1640s, "act of cutting off," also "portion cut off," from verbal phrase cut off (see cut (v.) + off (adv.)). Sense of "new and shorter channel formed on a river" (especially the Mississippi) is from 1773; of road that cut off or shorten a route, from 1806; of clothing (adj.), from 1840. Cutoffs "jeans or other long pants trimmed down to be shorts" is by 1967.

The verbal phrase is attested from late 14c. as "detach by cutting;" from 1570s as "exclude from access" and "bring to an abrupt end;" and from 1590s as "intercept, stop the flow or passage of."

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kick-off (n.)
also kickoff, kick off, 1857, "first kick in a football match," from kick (v.) + off (adv.). The verbal phrase also is from 1857. Figurative sense of "start, beginning event" is from 1875.
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bug off (v.)
"leave quickly," by 1956, perhaps from bugger off (see bugger (v.)), which chiefly is British (by 1920s) but was picked up in U.S. Air Force slang in the Korean War. Also see bug (v.3). To bug out "leave quickly, scram" is from 1953.
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off-duty (adj.)

"not employed or occupied with one's normal work," 1743, from off (prep.) + duty.

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