Even sooner: When a car leaks oil onto one of these roads will that oil subsequently become radioactive for quite some time?

Water isn't as much of an issue because H20 will evaporate, break apart, and diffuse out into the wider world pretty fast (so diluted I doubt it would matter... Since it's radium, not uranium). Oil, on the other hand will stick around for a long ass time and slowly work its way out into the surrounding environment.

The same is true for all the pollution/particles from tires.