"cylinder of wood or metal with a spiral ridge round it; hole in which a screw turns," c. 1400, scrue, from Old Frenchescröe, escroue "nut, cylindrical socket, screwhole," of uncertain etymology; not found in other Romanic languages. Perhaps via Gallo-Roman *scroba or West Germanic *scruva from Vulgar Latin scrobis "screw-head groove," in classical Latin "ditch, trench," also "vagina" (Diez, though OED finds this "phonologically impossible").
Kluge, Watkins and others trace it to Latin scrofa "breeding sow," perhaps based on the shape of a pig's penis (compare Portuguese porca, Spanish perca "a female screw," from Latin porca "sow"). Latin scrofa is literally "digger, rooter," from PIE root *sker- (1) "to cut." A group of apparently cognate Germanic words (Middle Low German, Middle Dutch schruve, Dutch schroef, German Schraube, Swedish skrufva "screw") are said to be French loan-words.
Sense of "means of pressure or coercion" is from 1640s, probably in reference to instruments of torture (such as thumbscrews). Meaning "prison guard, warden" is 1812 in underworld slang, originally in reference to the key they carried (screw as slang for "key" attested from 1795). Slang meaning "an act of copulation" is recorded from 1929 (meaning "a prostitute" is attested from 1725). To have a screw loose "have a dangerous (usually mental) weakness" is recorded from 1810.
suffix in pet proper names (such as Johnny, Kitty), first recorded in Scottish c. 1400; according to OED it became frequent in English 15c.-16c. Extension to surnames seems to date from c. 1940. Use with common nouns seems to have begun in Scottish with laddie (1546) and become popular in English due to Burns' poems, but the same formation appears to be represented much earlier in baby and puppy.