Can smelling diesel be toxic, or is it only bad after it comes out as exhaust?

The spill on the street outside your house is an irritating annoyance, but it is far less dangerous than diesel exhaust, and will eventually dissipate. You could run in place over it for hours with no more ill effects than a headache and maybe a mildly scratchy throat. Consider the people who deal with large volumes of diesel fuel daily, and still have very long lifespans.