Screwed
late Middle English (as a noun): from Old French escroue ‘female screw, nut’, from Latin scrofa, literally ‘sow’, later ‘screw’. The early sense of the verb was ‘contort (the features), twist around’ (late 16th century).
wiktionary
(This etymology is missing or incomplete. Please add to it, or discuss it at the Etymology scriptorium. Particularly: “The reference given does not support most of the claims.”) From screw + -ed.
etymonline
screwed (adj.)
1640s, "strained or forced to the highest pitch" (a sense now obsolete;" past-participle adjective from screw (v.) By 1690s, of the face, eyes, etc., "twisted, contracted;" by 1770 as "attached or fastened with screws;" slang sense of "drunk, intoxicated" is by 1833. The verbal phrase screwed up earlier meant "tuned to a high or precise pitch" (1907), a figurative image from the pegs of stringed instruments; the meaning "confused, muddled" is attested by 1943.