This is from Andrew Seidel of the Freedom From Religion Foundation. A taste:
The spoken words have been as deliberate as the written words. We know that Washington didn’t add the words to the oath. Edward Lengel, former editor-in-chief of the Papers of George Washington project, concluded, “any attempt to prove that Washington added the words ‘so help me God’ requires mental gymnastics of the sort that would do credit to the finest artist of the flying trapeze.”
Like so much U.S. mythology, including Rip Van Winkle, Ichabod Crane, and the Headless Horseman, we owe this Washingtonian myth to Washington Irving.
American Creation's Ray Soller has done a great deal of very important detective work over the years on this issue.