Burnt stainless steel can easily be cleaned by applying white vinegar to a soft cloth and rubbing until clean. Finish by thoroughly drying with a fresh soft cloth.
Baking soda also works very well for cleaning stainless pots and pans. Try simmering baking soda and water together for a while, then leave the mixture to cool, soaking overnight if necessary.
Another method to try is to simmer cola in the affected pots or pans. Start by simmering the cola for several minutes. When finished, scrape clean and wash the pot or pan.
If you're running short on cleaning supplies, it's possible to remove the burnt-on substances using just dish soap and water. Simmer the soap and water together for a few minutes, then try to scrape clean with a scrubber. If you have trouble cleaning using this method, leave the mixture to soak overnight and then repeat the steps.
If you're dealing with remaining burnt-on stains, consider buying some oxygen bleach. Oxygen bleach is available in both liquid and powder forms. To use it for cleaning stainless steel, mix the bleach with dish soap and hot water. After leaving the mixture to work for a while, scrape the remaining burnt portions clean.