I actually make my own soaps with a version that can break down any grease including thick car grease. It helps break it down so it is safer for the environment.
However for small light oil grease including cooking oil you can use Dr. Bronner's Soap.
For personal use, Dr. Bronner's Soap is very drying. Not something I recommend unless you know how to dilute it.
I will make a post on Dr. Bronner's Soap one day when I get a chance.