If your vehicle is showing strong smell of burning oil from outside the car after driving, here are the most likely causes and the parts you'll need to fix each one.
The valve cover gasket degrades and hardens over time, allowing engine oil to seep out and drip directly onto the hot exhaust manifold, where it instantly burns off.
Oil spilled around the filler cap during a recent oil change, or a loose oil filter/drain plug, can cause oil to run down the engine block and hit the hot exhaust.
The gasket sealing the bottom of the engine can fail, allowing oil to leak and blow backward onto the hot exhaust pipes underneath the car while driving.
The seal at the rear of the engine wears out on higher mileage vehicles, leaking oil between the engine and transmission that gets blown onto the exhaust system.
Worn camshaft seals can allow oil to leak down the front or side of the engine block, eventually making its way to hot exhaust components as you drive.
On turbocharged vehicles, the oil feed or return lines can leak directly onto the extremely hot turbocharger housing, creating a strong burning smell and often visible smoke.