I would try your sewing machine oil on the residue after you've removed as much of the "sticky stuff" as possible. Apply the oil and let it soak in if you need to (works really well on old stickers and tape residue as well). You might need to use something like an old credit card to scrape up the adhesive. Work in small areas at a time otherwise you'll just get a mess.
If you had sticky stuff on anything other than your sewing machine, I'd tell you to use plain old cooking oil. It is an old trick (like peanut butter for gum in the hair) but it works.