for oil/grease fire, you want to use a specific fire extinguisher. specifically the foam extinguisher, dry powder extinguisher, and CO2 extinguisher.
in the absence of such things, dirt would be a good option. fire blanket can also be used. baking soda can also be used, but most household don't have the required amount. if the fire is small(on your sauce pan for example), simply covering it with the lid should cut the oxygen.
never use dynamite. i know this is common sense and intended as a joke, but the amount of people without brain is increasing by the day.
source : worked as a chef on a cruise ship for 3 years