"parti-colored, variegated with spots of different colors," late 14c. (early 14c. in surnames), as if it were the past participle of a verb form of the Middle English noun pie "magpie" (see pie (n.2)), in reference to the bird's black and white plumage. Earliest use is in reference to the pyed freres, an order of friars who wore black and white. Also in pied piper (1845, in Browning's poem based on the German legend; used allusively by 1939).
the common European jay (Garrulus glandarinus), early 14c. (late 12c. as a surname), from Old North French gai, Old French jai "magpie, jay" (12c., Modern French geai), from Late Latin gaius "a jay," probably echoic of the bird's harsh warning cry and supposedly influenced by Latin Gaius, a common Roman proper name.
For other bird names from proper names, compare martin and parrot. Applied to the North American blue jay (Cyanocitta cristata) from 1709; it is unrelated but has similar vivid markings, is noisy and restless, and also has a harsh call. Applied to humans in sense of "impertinent chatterer, loud, flashy dresser" from 1520s. Jolly as a jay was a Middle English expression for "very happy, joyful."
c. 1300 (probably older; piehus "bakery" is attested from late 12c.), "baked dish of pastry filled with a preparation of meats, spices, etc., covered with a thick layer of pastry and baked," from Medieval Latin pie "meat or fish enclosed in pastry" (c. 1300), which is perhaps related to Medieval Latin pia "pie, pastry," also possibly connected with pica "magpie" (see pie (n.2)) on notion of the bird's habit of collecting miscellaneous objects.
According to the OED, the word is not known outside English with the exception of Gaelic pighe, which is from English. In the Middle Ages, a pie had many ingredients, a pastry but one. Fruit pies began to appear c. 1600.
The word in the figurative sense of "something easy" is from 1889. Slice of the pie in the figurative sense of "something to be shared out" is by 1967. Pie-eyed "drunk" is from 1904. Phrase pie in the sky is attested by 1911, from Joe Hill's Wobbly parody of hymns. Pieman "baker or seller of pies" is by c. 1300 as a surname. Pie chart is from 1922.