1590s, "slender riding whip," probably from a Flemish or Low German word akin to Middle Dutch swijch "bough, twig," or swutsche, variant of Low German zwukse "long thin stick, switch," from Germanic *swih- (source also of Old High German zwec "wooden peg," German Zweck "aim, design," originally "peg as a target," Zwick "wooden peg"), perhaps connected with PIE root *swei- (2) "to swing, bend, to turn."
The meaning "device for changing the direction of something or making or breaking a connection" is first recorded 1797. "The peg sense suits the mech(anical) applications" [Weekley]; also compare switchblade. These senses in English might be a direct borrowing from those senses in Continental Germanic languages rather than a continuation of the "pliant wand" sense. The meaning "a change from one to another, a reversal, an exchange, a substitution" is first recorded 1920; extended form switcheroo is by 1933.
1610s, "to strike with a switch," from switch (n.). Related: Switched; switching. The meaning "turn (off or on) with a switch device" is first recorded 1853 of trains on tracks, 1881 of electricity, 1932 of radio or (later) television. Sense of "shift, divert" is from 1860. Meaning "to change one thing for another" is recorded from 1919. Switch-hitter is 1945 in baseball slang; 1956 in the sense of "bisexual person."