"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" [1889] describes the noun as an American term of contempt for a person, "a sham 'swell;' a simpleton," and suspect it might be from jayhawker.

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."

"freebooter, guerrilla," American English, 1858, originally "irregular or marauder during the 'Bleeding Kansas' troubles" (especially one who came from the North). It seems to have come into widespread use only during the Civil War. There was said to have been a bird of this name, but evidence for it is wanting. Perhaps a disparaging use from jay (n.). Hence back-formed verb jayhawk "harass" (1866).

Bushwhackers are men, united together, but not soldiers, who live in the bush; and whose avowed object is to kill every Union soldier they can, and cripple, so far as they can, the resources of the Federal military power. The jayhawkers are thieves. They plunder indiscriminately from all parties. In the same band are both rebel and Union men. ... Guerilla bands are companies enlisted and sworn into the rebel service; but not belonging to the armies. [Henry M. Painter, "Brief Narrative of Incidents in the War in Missouri," Boston, 1863.]

by 1912, American English, first attested in baseball slang; as a type of music, attested by 1915. Perhaps ultimately from slang jasm (1860) "energy, vitality, spirit," perhaps especially in a woman. This is perhaps from earlier gism in the same sense (1842).

By the end of the 1800s, "gism" meant not only "vitality" but also "virility," leading to the word being used as slang for "semen." But — and this is significant — although a similar evolution happened to the word "jazz," which became slang for the act of sex, that did not happen until 1918 at the earliest. That is, the sexual connotation was not part of the origin of the word, but something added later. [Lewis Porter, "Where Did 'Jazz,' the Word, Come From?" http://wbgo.org Feb. 26, 2018]

Meaning "rubbish, unnecessary talk or ornamentation" is from 1918. Slang all that jazz "et cetera" first recorded 1939. Further observations from Porter's summation of the research:

"Jazz" seems to have originated among white Americans, and the earliest printed uses are in California baseball writing, where it means "lively, energetic." (The word still carries this meaning, as in "Let’s jazz this up!") The earliest known usage occurs on April 2, 1912, in an article discovered by researcher George A. Thompson, and sent to me courtesy of [Professor Gerald ] Cohen.

... By 1915, jazz was being applied to a new kind of music in Chicago.  It seems to have been first applied to Tom Brown's all-white band, which hailed from New Orleans. This was followed by many printed references to jazz as a musical style.