If you're just going by what literally has the word wheel in it, your car only has one wheel: the steering wheel. The four tires on it don't count, because they're clearly tires and not wheels.

Like, yes, if you arbitrarily limit a definition, you can skew results however you want. But a wheel is a circular device capable of rotating on its axis, facilitating movement or transportation or performing labour in machines. That definition would include gears, tires, the wheels guiding your timing belt, arguably the stereo and thermostat knobs. So, yes, your vehicle probably does have many more wheels in it than you'd care to count.

I mean, the definition of a wheel is given as:

a circular frame of hard material that may be solid, partly solid, or spoked and that is capable of turning on an axle

The little wheels on the runners definitely count since they fit the definition just fine.

But that's also kind of the point, the question is so hard to answer because people can keep thinking of more doors or wheels they hadn't considered yet. The question itself invites silliness, that's its appeal.