Green’s Dictionary of Slang

1. squinting, crooked.

1890–1904		Farmer & Henley Sl. and Its Analogues.
1906		Burlingame Enterprise (KS) 23 Aug. 2/3: If the lines of the waist be skewgee [...] the dress will make the woman who wearsit a caricature.
1912		Dly Press (Newport News, VA) 6 Oct. 15/3: A man was plowing. He had fastened the reins across his shoulders [...] but the reins were all skewgee.
1915		M.G. Hayden ‘Terms Of Disparagement’ in DN IV:iii 219: skew-gee, -jaw, [...] awry, twisted. ‘Your tie is all skew-gee.’.
1949		News-Jrnl (Mansfield, OH) 8 May n.p.: No proponent of liberty [...] stood up [...] without being knocked skewgee.
1950		Des Moines Trib. (IA) 8 Sept. 13/6: The new iowa Power and light Building [...] has its first floor show window set ‘skewgee,’ instead of flush with the facade.
1963		Decatur Herald (IL) 10 Jan. 48/3: The lines weren’t always plumb. When the roof was too much on the skewgee, the neighbors would remark ‘that there barn is sure sigogglin’’.

2. mixed-up, confused.

1897		E.W. Brodhead Bound in Shallows 165: When folks get all skew-gee brooding on things, why, it seems only right to straighten ’em out [DA].
1908		Aberdeen People’s Jrnl 29 Aug. 12/4: Giving her forehead a little tap, as much asd to say ‘something skee-gee in Mrs Brown’s brain’.
1909		Baxter Springs News (KS) 15 July 4/4: I’d had a skewgee day at the office.
1919		Middletown Dly Herald (NY) 22 Aug. 5/2: The world isn’t all awry and skewgee and out of gear.