Do I need a visa for the approx. 84 hours that I am in Shanghai before flying home to the U.S.?

If the last country you fly from before entering Shanghai is not USA, you can enjoy 144 hour free transit in there, no need to apply for a visa for that.

We fly from the U.S. on Oct. 3 for Tokyo, to board the ship, we are making stops in Japan and S. Korea by ship and then getting off the ship in Shanghai and staying there for 2 nights and then flying home.

Still not clear with your answer to me Jessica. Do I need a visa or not and if not how do I get the 144 hour pass? Thanks, Harriet

You can enjoy 144 hour free transit in Shanghai. When you board the ship in Japan, you need to inform the carrier that you want to use the 144 hour free transit in Shanghai. After arriving at SH port, you can go to the transit counter to apply for the 144 hour free transit.