In most cataclismic sci-fi cars seem to be of little or no importance, which makes sense given that most countries have no oil themselves and even for those which do, the ability of actually extracting the stuff from the current hard to reach modern reserves (the stuff doesn't just boil out of the ground nowadays) and refining it isn't likely to be available at all for what's left of society.

Curiously, electric cars and solar panels make post-catacysmic use of cars more likely than the ICE engine of the cars in Mad Max.

That said, given enough time whatever stock of solar panels use will be gone to just natural degradation and exposure to the elements and the technology to do more won't be there anymore (though wind and water generation would still be possible), plus the roads themselves will become unusable as Nature does its thing.

The most likely Mad-Max post-cataclismic future will be using animal-drawn vehicles or just people riding the animals.