I bring this up because I recently saw a picture of Harding shaking hands with Einstein, I have no clue what to make of it, anyone know?

Einstein came to the US about the time of Harding's administration so my guess is he was welcoming the famous scientist to America.

Well. maybe I don't know my history, but I've always been told that Einstein came to the U.S at the break of WWII, maybe what happened is he left during the time of Nazi takeover...

Here's your answer:

http://www-groups.dcs.st-and.ac.uk/~.../Einstein.html

During 1921 Einstein made his first visit to the United States. His main reason was to raise funds for the planned Hebrew University of Jerusalem. However he received the Barnard Medal during his visit and lectured several times on relativity. He is reported to have commented to the chairman at the lecture he gave in a large hall at Princeton which was overflowing with people:-

"I never realised that so many Americans were interested in tensor analysis."

Also..

By 1930 he was making international visits again, back to the United States. A third visit to the United States in 1932 was followed by the offer of a post at Princeton. The idea was that Einstein would spend seven months a year in Berlin, five months at Princeton. Einstein accepted and left Germany in December 1932 for the United States. The following month the Nazis came to power in Germany and Einstein was never to return there.

So he arrived here 7 years before WWII. Evidently he met Harding on his first visit here.

Thanks for the input