What is the exact meaning of a "Prof. Dr. med. Dr. med. dent. Dr. med. habil."?
The usual doctoral degrees in medicine and dentistry in the U.S. are not Ph.D.'s but M.D. and D.D.S. (for "medical doctor" and "doctor of dental surgery" or some Latin variant of those). So I'd use those to translate Dr. med. Dr. med. dent.

As for habilitation, I don't know exactly what it involves in medicine, but in mathematics it indicates research accomplishment after the doctoral degree. In many cases, it involves a second thesis ("Habilitationsschrift" in German), but it can also be just a collection of published papers.  I imagine medicine is similar, but I have no real knowledge of that.