From Random House Dictionary of Historical American Slang J.E.Lighter ed., 1997, page 147.

hoolihann. West 1. (among cowboys) (see 1985 quot.). 1910 in Lomax and Lomax Amer. Ballads 384: I am a-riding old Paint, I am a-leading old Dan,/I'm goin' to Montan' for to throw the hoolihan. 1985 H. Cannon Cowboy Poetry138: Hoolihan backhand thrown loop for roping horses.

2. an exciting or extraordinary event. 1973 F. Carter Outlaw Wales 182; Seen him take on five pistoleros. He got three of 'em before they cut him down....It was a real hoolihan.

throw the hoolihan [fr. sense of (1), (among cownboys) to celebrate riotously. 1944 R. Adams Western Words:Houlihan, throw the.... to paint the town red.

hoolihan v. [perh. obscurely fr. Houlihan, Irish family name] West. to bulldog (a steer) by bringing it to the ground without twisting its neck.
1925 W.James Drifting Cowboy 105; I hoolyhanned him on the jump and busted him right there. 1933 J.V.Allen Cowboy Lore 12:Hoolihaning is the act of leaping forward and alighting on the horns of a steer in bull-dogging in a manner to knock the steer down without....twisting the animal down with a wrestling hold. Hoolihaning is banned at practically all recognized contests. 1936 McCarthy Mosshorn unp.):Hoolihaning. The old-time practice of bulldogging.