Old English crawe, imitative of bird's cry. Phrase eat crow is perhaps based on the notion that the bird is edible when boiled but hardly agreeable; first attested 1851, American English, but said to date to War of 1812 (Walter Etecroue turns up 1361 in the Calendar of Letter Books of the City of London). The image of a crow's foot for the wrinkles appearing with age at the corner of the eye is from late 14c. ("So longe mote ye lyve Til crowes feet be growen under youre ye." [Chaucer, Troilus and Criseyde, c. 1385]). Phrase as the crow flies recorded from 1800.
Old English crawian "make a loud noise like a crow" (see crow (n.)); sense of "exult in triumph" is 1520s, perhaps in part because the English crow is a carrion-eater. Related: Crowed; crowing.