How to get burnt food off my nonstick pan?

A bit of household hydrogen peroxide, enough to cover to about 1/4 inch...a pinch of baking soda. And warm it up to activate it, it'll release the carbon bonds. It'll stink while it heats up, and you don't need a lot of heat...just slight warm until it starts bubbling. Then cool for 30 mins. The carbon should lift right out.

What you have are carbonization stains/streaks, which can be tough to get off. I suggest applying a paste of something like Bon-Ami, and letting it sit for at least 10 minutes or so before scrubbing away. You can also try using a combination of 1/2 cup vinegar and 1 1/2 cup water, brought to a boil, and then allowed to cool. That may also help remove or loose the material.

You could try a dobie sponge - yellow sponge with white nylon mesh over it that won't scratch your pan. The interweb says to sprinkle it with baking soda, put a few tablespoons of water over it and soak it overnight