Sorry PA - I should have said your thirst for knowledge is quite sane

'Here I sit - I've got the brain the size of a planet

And all they want me to do, is to make the tea'

Marlon - the paranoid android from Hitchhikers guide

Here's some dafter ideas:

It stands for Old Kinderhook, the nickname of Martin Van Buren who came from Kinderhook, New York. Old Kinderhook played a role in popularizing the term, but it is not its origin. (More on this later.)

It comes from any one of a number of languages, most often the Choctaw word okeh. This explanation often involves Andrew Jackson again, but this time adopting it from the Indian language not because he was orthographically-challenged. A later president, Woodrow Wilson, favored this explanation, but he was wrong. As far as this explanation goes, it was not suggested until 1885 and no evidence exists that this, or any foreign word, is in fact the origin.

It is an abbreviation for Oberst Kommandant, or Colonel-in-Command, used by Von Steuben or Schliessen (take your pick) during the Revolutionary War. No record of either man, or anyone until 1839, using this phrase exists.

It comes from the French Aux Cayes, a port in Haiti famed for its rum.

It stood for Orrin Kendall crackers supplied to the Union Army during the Civil War. Unfortunately for Orrin's immortality, OK was in use twenty years before the Civil War.

It stood for Obadiah Kelly, a railroad shipping clerk akin to Kilroy who initialed bills of lading. And,

That it was an 1860s telegraph term for Open Key.