Old English strica "line of motion, stroke of a pen" (related to strican "pass over lightly"), from Proto-Germanic *strikon- (source also of Middle Dutch streke, Dutch streek, Middle Low German streke "a stroke, line," Old High German, German strich, Gothic striks "a stroke, line"), from PIE root *strig- "to stroke, rub, press" (see strigil; also compare strike (v.), stroke (v.)). Sense of "long, thin mark" is first found 1560s. Meaning "a temporary run (of luck)" is from 1843.
1768, "to go quickly, to rush, run at full speed," respelling (probably by association with streak (v.1)) of streek "to go quickly" (late 14c.), originally "to stretch oneself" (mid-13c.), a northern Middle English variant of stretch (v.). Related: Streaked; streaking.