Baking soda or barkeeper's friend with a mesh metal scrubber.
Try scrubbing with baking soda.
Here is a how-to:
Make a paste of baking soda and a little water, apply a heavy layer, let it set at least 8 hours, scrub with the rough side of a dollar store sponge. Repeat if needed.
Bonnie...Barkeepers Friend from most grocery stores should help you,
Stainless steel is super easy to clean because you don't have to be gentle with it. Let it soak with hot water and baking soda. Then scrub it with a brush or sponge.
I use Cerama Bryte. It works amazingly on many household items and makes my pots shine.
hometalk has some ideas:
Bar Keepers Soft Scrub.