Green’s Dictionary of Slang

1. of a venue, full, a full house.

1902		Ade Forty Modern Fables 70: Mazie had such a Rush of Men Callers that the S.R.O. Sign was out almost every Night.
1915		O.O. McIntyre Day By Day in New York 11 Mar. [synd. col.]He invited morris to come over to his theater and see the S.R.O. sign out nightly.
1934		Charleston (WV) Daily Mail 31 July 6/8: S.R.O. means ‘standing room only.’.
1946		C.S. Montanye ‘Don’t Meddle with Murder’ in Thrilling Detective May 🌐 ‘Lady in Love’ was strictly S.R.O. at every performance.
1959		‘Paul Merchant’ ‘Sex Gang’ in Pulling a Train’ (2012) [ebook] There was a silent [...] order to ‘move ’em out’ [i.e. brothel customers] after they’d had their jollies, to allow the SRO crowd bed-space.
1988		D. Woodrell Muscle for the Wing 145: St. Peter’s was SRO, for the Langlois clan was large and widespread.
1990		(con. early 1950s) J. Ellroy L.A. Confidential 26: The party in full swing, the muster room SRO.
2001		(con. 1964–8) J. Ellroy Cold Six Thousand 6: SRO — big barside numbers.

2. describing anything that sells out or is very popular.

1978

Time 2 Oct. 88: Pronto, a trendy East Side Italian restaurant, is offering a Sunday brunch for the first time, and similar affairs at other nosheries are S.R.O.