There is a nautical source from the days of sailing ships, pertaining to a ships being rigged to catch the wind in a certain way, but for a person to be squared away is a military term. Squared away pertains to two things, perfect square corners to the sheets on your cot and during the First World War the ground sheet you carried was folded into a perfect square and placed flat against your back. So in the military services in the U.K. to have your things in order and tidy was to be 'squared away'.
Some of this is interesting, some needs spoiler tags, some like this puts me to sleep as I type it.....
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