It's believed that askew was formed simply by attaching the prefix "a-" (meaning, among other things, "in (such) a state of condition) to the word "skew" (meaningto be out of alignment or at an angle).  Theword skew, which derives via Middle English from Anglo-French eschiver, meaning "to escape or avoid," can be a verb, adjective, or noun. 

The word "askew" was first used in English in the mid-16th centruy, around 1565.  It is believed to have originated from the Old Norse phrase "á ská," meaning "on a skew". 

Examples of askew used in a sentence: 
"He askew them what was the matter."
"Her works are noted for their slightly askew plots and exploration of the human psyche." 
"The first one went a bit askew."  
"Are the plates for light switches and outlets square or slightly askew?" 
"My eyes stuck on the bow tie, because it was slightly askew." 
"He still wore his suit, his tie only slightly askew."  
"It was then that he noticed the slightly askew vent cover."