mid-14c., "direct, undeviating, not crooked," properly "that which is stretched," adjectival use of Old English streht (altered, by analogy with streccan, from earlier streaht), past participle of streccan "to stretch" (see stretch (v.)). Meaning "true, direct, honest" is from 1520s. Of communication, "clear, unambiguous," from 1862. Sense of "undiluted, uncompromising" (e.g. straight whiskey, 1874) is American English, first recorded 1856.
Theatrical sense of "serious" (as opposed to popular or comic) is attested from 1895; vaudeville slang straight man first attested 1923. Go straight in the underworld slang sense is from 1919; straighten up "become respectable" is from 1907. Straight arrow "decent, conventional person" is 1969, from archetypal Native American brave name. To keep a straight face first recorded 1897; straight shooter is from 1928; straight-edge as a punk subculture is attested by 1987.
Very strict in one's military appearance and grooming
[1970s+ Army; fr STRAC, acronym for Strategic Army Corps, chosen units in constant combat readiness, hence elite troops]