Since you asked...CV axle boots contain grease. If the boot ruptures/tears, then it will sling the grease all over the place. If it gets onto a hot part, like a catalytic converter, then it will bake, cause smoke, and smell. Grease, like oil, is a petroleum-based substance.
Rizzo, it doesn't sound like your car is burning oil internally, especially if you're not getting smoke out of the exhaust pipe. Is it for sure motor oil that is being burned on a hot part under your car? Could be rear main, valve cover gasket, etc, if it's motor oil. I recently replaced my entire steering rack due to it hemorrhaging PS fluid all over the main cat. Lots of fun smoke and burning smells.
I guess look under it, and see if you can locate a leak source.