http://www.martinmarietta.com/products/MSDS-Asphalt.pdf
"In general, the oxidation of polycyclic aromatic hydrocarbons destroys their carcinogenic potential."
Personally, I don't worry about asphalt, especially old asphalt covered in dirt/dust. However, I avoid fresh asphalt while it's still airing out, as that stuff smells pretty nasty.
My soles get a bit dusty, and I'll wash them off with soap and water. As for your gunk, who knows? Just how gunky do they get? Do you run on industrial roads? Perhaps, consider contacting an analytical testing lab, if you are worried enough.
Personally, I don't run on busy roads, because I don't like breathing in exhaust and particulates.
www.msdsonline.com/blog/2010/08/does-osha-require-an-msds-for-exhaust/