Old English strican (past tense strac, past participle stricen) "pass lightly over, stroke, smooth, rub," also "go, move, proceed," from Proto-Germanic *strikan- (source also of Old Norse strykva "to stroke," Old Frisian strika, Middle Dutch streken, Dutch strijken "to smooth, stroke, rub," Old High German strihhan, German streichen), from PIE root *strig- "to stroke, rub, press" (see strigil). Related to streak and stroke, and perhaps influenced in sense development by cognate Old Norse striuka.
Sense of "to deal a blow" developed by early 14c.; meaning "to collide" is from mid-14c.; that of "to hit with a missile" is from late 14c. Meaning "to cancel or expunge" (as with the stroke of a pen) is attested from late 14c. A Middle English sense is preserved in strike for "go toward." Sense of "come upon, find" is from 1835 (especially in mining, well-digging, etc., hence strike it rich, 1854). Baseball sense is from 1853. To strike a balance is from the sense "balance accounts" (1530s).
Meaning "refuse to work to force an employer to meet demands" is from 1768, perhaps from notion of striking or "downing" one's tools, or from sailors' practice of striking (lowering) a ship's sails as a symbol of refusal to go to sea (1768), which preserves the verb's original sense of "make level, smooth."