One method is to use the lye present in the ashes of many hardwood trees to saponify (residual) oils in your cooking pot. It doesn't need to be a precise blend; simply mix some water, ashes, and oil into a paste and use that to scrub. It's not as harsh a scouring powder as sand or salt, and won't scratch the metal, which can make everything stick.

Also deglazing a still hot pot or pan with cool liquid is not only a great way to free cooked on bits, but add a flour slurry and you've made gravy!