This colloquial expression for something crooked or askew dates from eighteenth-century Scots and is now mainly to be found in Britain and the Commonwealth.
You’ll think you’ve tumbled into a Vermeer with your first glimpse of a skinny townhouse so skew-whiff that it’s probably only standing by dint of being supported on either side by equally historic homes.
The Scotsman, 20 December 2008.
The off-centredness is often figurative. One writer described a pop song as having “skew-whiff charms”; others variously criticised a skew-whiff shortlist, referred to a poem’s skew-whiff irony, and shuddered at fashion’s “skew-whiff combos like puce and purple”.
The first part of the word will cause no difficulties, since it is almost certainly from askew. The second element, I am assured by those who know (though most dictionaries dodge the issue), is the same word as that meaning a light puff of air, suggesting that the thing in question has been blown off course.
A few North Americans may know the closely related skewgee or similar words with variable spellings. Here, the second part is from the Scots agee (or ajee), created from a call to a horse to move to one side.