If the drain plug on your vehicle is above the exhaust, it would most likely cause a burning smell, but on my Contour (V6) the drain plug isn't located that way. However, the drain plugs are fitted with a rubber gasket, so if you're able to get under the car you would see oil around the plug if it's leaking.
Have you noticed that the car is losing oil? If so, oil on any part of the engine block/heads would burn & cause a smell, not just on the exhaust. Check around the engine to see if there is any oil on it, which would probably indicate a leaking gasket.
Hope this helps!
