Green’s Dictionary of Slang

Hogan’s goat n.

[a fanciful animal owned by a fictitious Irishman]

1. (US) one who interferes or ‘butts in’.

[US]F. Hutchison Philosophy of Johnny the Gent 50: ‘[I]n blows 'bout half a dozen o’ them long haired college kids [...] Well, the original Hogan’s goat, Mr. Wise Crackin’ Kid, has to butt in wit’ them’.

2. (US) an obnoxious thing; thus stink like hogan’s goat v., to be bad, objectionable, a failure etc.

[US]Funk Heavens to Betsy 98: When one says that a given TV show, movie, book, or whatever, is ‘like Hogan’s goat,’ he is with reasonable politeness saying that ‘it stinks terrifically’ [DARE].
[US](con. early 1950s) J. Peacock Valhalla 500: That new bunch has fucked me up more than Hogan’s goat.
[US] in DARE.
[US]Mother Jones IV:1 18: ‘This thing was more screwed up than Hogan’s goat,’ screamed Brattleboro’s fire chief.
[US]B. Bowles They Love a Man in the Country 66: I’ll be deader than Hogan’s goat come next January when I come out of office.
[US]R.C. House Trackdown at Immigrant Lake 212: Trail’ll be colder than Hogan’s goat come morning, but what the hell.
[US]E.S. Connell Lost in Uttar Pradesh 162: The best and brightest had no more sense than Hogan’s goat.

3. (Irish) a kept woman.

[Ire]G. Coughlan Everyday Eng. and Sl. [Internet] Hogan’s Goat (phr): kept woman.