Sounds weird but to remove tape gunk try mayonnaise. I was told this trick when I had to remove a lot of duct tape gunk with marring the finish. I don't think I'd do this on wood but works well on metal. To finish the top and sides of the table since it'a already stripped I'd give it a very light sanding, wipe with tack cloth and to blend in the oil stains use wood stain to stain top and apply two coats of matte finish.