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c.1300, a shortening of Old French estraier "wander about," literally "go about the streets," from estree "route, highway," from Late Latin via strata "paved road" (see street). On another theory, the Old French word is from Vulgar Latin *estragare, a contraction of *estravagare, representing Latin extra vagari "to wander outside" (see extravagant). Figurative sense of "to wander from the path of rectitude" is attested from early 14c.
"domestic animal found wandering," early 13c., from Old French estraié "strayed," past participle of estraier (see stray (v.)). The adjective is first recorded c.1600.