First question - how certain are you the fluid or substance is engine oil? Check the smell and consistency - there are other possibilities; anti-freeze (coolant) from the heater core or heater hoses.
Check the radiator and cooling system for the antifreeze condition - there should be no corrosion or rust visible inside the engine, hoses, radiator, overflow reservoir (tank), and heater core.
Check the cooling system for any leaks by a pressure test, at the radiator or coolant overflow tank. Local auto parts stores can loan a cooling system pressure tester for a small cost.
If any leak is found, repair, or replace as required. New hose clamps and new radiator hoses are inexpensive insurance.
Next step, flush the system with an off-the-shelf cooling system cleaner (caustic) then flush with fresh water, then refill with the correct 50/50 mixture of antifreeze and water.
In addition, the radiator and cooling system should be cleaned / flushed and refilled according to the manufacturer maintenance intervals; typically every 24-36k miles. Check the vehicle owners manual for the specifics.