The type of oil that a 2 cycle engine takes is 2 cycle engine oil or 2 stroke engine oil which is commonly sold in small bottles.
Although you can buy quarts and even gallons of 2 cycle engine oil.
The 2 stroke engine oil is specially formulated for lubricating 2 stroke engines and is just the right thickness.
Running the wrong engine oil in a 2 stroke engine can damage it or cause the engine to not run at all.
A 2 cycle engine is lubricated through the carburetor and gasoline as it gets combusted.
Unlike a 4 cycle engine that has an oil pan and the oil gets thrown up unto the pistons etc to lubricate it the oil for the 2 cycle engine is mixed in with the gasoline and as the gasoline is burned the engine gets lubricated through the mix of the engine oil.
This is why it's important to mix the oil and gas properly as too little oil can cause the engine to not get enough lubrication.
Two-stroke engines use their crankcase to pressurize the air-fuel mixture before transfer to the cylinder.
Unlike four-stroke engines, they cannot be lubricated by oil contained in the crankcase and sump: lubricating oil would be swept up and burnt with the fuel.
A 2 stroke pulls air fuel down into the crankcase and pressurizes transfer ports.
That circulation of air /fuel mixture through the crankcase is all it takes to lube the bottom end.
it provides a light coating of oil.
A two stroke engine has neither and oil sump or pump.
The oil is added to the fuel and flows through the crankcase lubricating the moving parts before being burned in the combustion chamber.