Green’s Dictionary of Slang

1. (US) awkward, ungainly.

c.1850		F.M. Whitcher Widow Bedott Papers (1883) 45: The widder’s a skew-jawed oncomfortable lookin’ old critter, ain’t she?
1873		Kansas Trib. (Lawrence, KS) 23 Oct. 1/2: Why the Republicans [...] send to the legislature old knock-kneed, skew-jawed, broken-winded, crib-biting, political hacks, is one of the things a fellow can't understand.
1905		Democrat & Chron. (Rochester, NY) 29 May 25/3: ‘You know I xcan never stay in room where things are skew-jawed around’.

2. (US) confused, muddled.

1886		Richmond Item (IN) 8 Mar. 4/2: ‘Understand you got some of your texts a little skew-jawed Saturday, judge’.
1918		Star Trib. (Minneapolis, MN) 2 Jan. 6/4: He [...] gets his rifle and cannon calibers, and estimates skew-jawed.

3. (US) bent or twisted out of shape.

1891		Star-Democrat (Easton, MD) 4 Aug. 4/2: ‘I have a black eye, a swelled jaw, a skew-jawed nose and bruises all over me.
1966		Fort Lauderdale News (FL) 7 Mar. 3/1: Skew-jawed doors, and locks that didn’t work.