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."
"fourth-rate, worthless" (as in a jay town), 1888, American English, earlier as a noun, "hick, rube, dupe" (1884); apparently from some disparaging sense of jay (n.). Perhaps via a decaying or ironical use of jay in the old slang sense "flashy dresser." Century Dictionary (1890s) notes it as actors' slang for "an amateur or poor actor" and as an adjective a general term of contempt for audiences.
"A jay hasn't got any more principle than a Congressman. A jay will lie, a jay will steal, a jay will deceive, a jay will betray; and, four times out of five, a jay will go back on his solemnest promise. The sacredness of an obligation is a thing which you can't cram into no blue-jay's head." ["Mark Twain," "Blue-Jays"]
They were said to be disliked by hunters because their cries aroused deer. Barrère and Leland's "Dictionary of Slang, Jargon & Cant"  describes the noun as an American term of contempt for a person, "a sham 'swell;' a simpleton," and suspect it might be from jayhawker.