c. 1500, "strange, peculiar, odd, eccentric," from Scottish, perhaps from Low German (Brunswick dialect) queer "oblique, off-center," which is related to German quer "oblique, perverse, odd," from Old High German twerh "oblique" (from PIE root *terkw- "to twist"). For the suggested sense evolution, compare cross (adj.). But OED is against this etymology on grounds of timing and sense.
The meaning "appearing, feeling, or behaving otherwise than is usual or normal" is by 1781. The colloquial sense of "open to suspicion, doubtful as to honesty" is by 1740. As a slang noun, "counterfeit money," by 1812; to shove the queer (1859) was "to pass counterfeit money. Queer Street (1811) was the imaginary place where persons in difficulties and shady characters lived, hence, in cant generally, "contrary to one's wishes."
Sense of "homosexual" is attested by 1922; the noun in this sense is 1935, from the adjective. Related: Queerly. Queer studies as an academic discipline is attested from 1994.
Among the entries in the 1811 "Lexicon Balatronicum" are: Queer as Dick's Hatband "Out of order without knowing one's disease"; Queer Bitch "An odd out of the way fellow"; Queer Ken "A prison"; Queer Mort "A diseased strumpet"; Queer Rooster "An informer that pretends to be sleeping and thereby overhears the conversation of thieves in nightcellars."