Green’s Dictionary of Slang

(orig. US) an erection; the erect penis; also in fig. use, a thrill.

1944		in G. Legman Limerick (1953) 9: There was a young fellow named Goody / Who claimed that he wouldn’t, but would he? / If he found himself nude / With a gal in the mood, / The question’s not woody but could he?
1985		J. Wambaugh Secrets of Harry Bright (1986) 47: He noticed what was hanging down all pink and shiny below his Desmond’s belly. Old Desmond had sprouted a woody!
1994		D. Lehane A Drink Before the War 86: I said ‘What’s up?’ expecting he had something private to tell me. ‘Oh, nothing [...] I just do that [i.e. bluster aggressively] to show them who’s boss. It gives me a woody." .
1997		J. Birmingham Tasmanian Babes Fiasco (1998) 168: ‘[I] Pleaded with them [Church of Scientology] to get over there and get on his case because he had a lot of money to spend and he was very vulnerable.’ ‘Bet that gave them a woody.’.
1997		Roger’s Profanisaurus in Viz 87 Dec. n.p.: woody n. An erection.
2000		M.E. Dassad ‘Chickenhawk’ at www.cultdeadcow.com 🌐 I reluctantly pulled my woodie from her mouth and let her catch her breath as I rubbed the head of my cock over her face.
2004		C. Hiaasen Skinny Dip 169: The cruellest of afflictions, an enduring yet pleasureless woody.
2008		Simon & Burns ‘A Burning Dog’ Generation Kill ep. 5 [TV script] I get a woodie.
2015		S. King Finders Keepers (2016) 3: Old fella’s got a woody. Must have been having one hell of a dream.