Green’s Dictionary of Slang

(US) drunken; initiated by drunkenness; thus sogged adj., drunk; sog n., drunkenness.

1876		Oakland Trib. (CA) 19 June 3/1: In the Police Court [...] one unusually ‘soggy’ old drunk was fined $10.
1880		Chicago Trib. 10 Nov. 5/3: Waldron, soggy drunk, passed out.
1895		Fayette Co. Leader 14 Mar. 4/2: They did not get right down. Soggy drunk, exactly.
1899–1900		C.L. Cullen Tales of the Ex-Tanks 88: Alcoholism is inseparably mixed with any man’s desire to return to his old boyhood home [...] I know all about that soggy desire. [Ibid.] 89: I wasn’t sogged enough to feel like keeping on for the rest of the way. [Ibid.] 148: I had been indulging in two months of wooze and sog.
1902		Boston Post (MA) 8 Mar. 11/2: Four drunks, hopelessly sogged with liquor.
1903		L.A. Times 3 Sept. 14/3: Campbell [...] getting soggy drunk [...] drunk and ugly.
1915		Dly Arkansas Gaz. (Little Rock, AR) 17 Jan. 30/5: ot only was Fiddles drunk, asoggy, hopelessly drunk, but [etc].
1920		H. Wiley Wildcat 79: They’s willin’ boys, but they’s soggy wid ruckus juice.
1950		Pittsburgh Press (PA) 20 Feb. 15/3: The Saga of the Soggy Housewife — Home Drunk from Maternity Ward.
1977		Orlando Sentinel (FL) 19 Mar. 24/2: ‘What are you doing to do? Be a soggy drunk or a nice person’.