Cooking oil is nowhere near as volatile as petrol/gasoline, meaning it doesn't readily evaporate and form explosive mixtures with air like petrol does. If it did, turning on a stove or fryer would ignite it like petrol in the engine and blow up the kitchen, haha. Cooking oil is more like diesel fuel, it has a much higher evaporation temperature/ lower evaporation pressure and flash point than petrol, so it won't vaporize adequately enough inside the cylinder to burn, nor will a spark plug produce a hot enough spark to ignite much of it. If you tried to do that, at best your car would run like crap and trash a catalytic converter, at worst you'd damage the engine or need a very expensive overhaul to get all of the vegetable oil out. It will not run with much oil in it. That will work with a diesel engine that's been correctly modified, since the compression gets high enough to self-ignite diesel oil, but it will just make a mess out of your gasoline/petrol engine. 

If you're talking about running an old diesel on waste cooking oil it can be done, in fact a friend of mine did it years ago with an old diesel Volvo. Smelled like french fries when he drove by. You don't mix gasoline in with it though! It needs to be strained and filtered, and some provision for keeping it liquid it has to be made in cold weather. (Heating it or mixing with diesel fuel.)

https://www.youtube.com/watch?v=WNJH1rikujI

It's not a 2 stroke engine, but go ahead if you want to destroy your engine

Typically the word petrol means gasoline in the states. If it is a gasoline engine then you can't mix cooking oil with the fuel. If it is a diesel engine which is much more common in the EU and Asia you can mix it with diesel fuel but understand cooking oil typically contains a lot of solids that will clog your fuel filter and cause other problems. It also has a tendency to gel in cold weather. The amount you save may be offset by repair costs. As a general rule never run an engine on anything other than the manufacturers recommendation.