If your table top is veneer, use chemicals to strip it. You want to avoid doing any aggressive sanding that can sand through the veneer. Apply citris stripper and let it sit overnight.

I'd try some lacquer thinner. Outside, please.

Try some Googone.

There are a few ways to remove leftover vinyl adhesive from a table. One way is to use a hot iron and paper towel. Place the iron on the highest setting and place the paper towel over the adhesive. Hold the iron in place for about 10 seconds, then remove the paper towel and adhesive should come off with it. Another way is to use Goo Gone. Apply Goo Gone to a cloth and rub it over the adhesive. The adhesive should come off with the Goo Gone.