Yes, there are Dodge class As out there from the 70s and earlier.
Class C of that era will most likely be a 440 or a 360.
If it's a class C, it will be on a B300 sportsman van chassis. If it's a class A it will be a MB300 chassis.
For tires, the only 16.5 tire still being manufactured with the rating needed for a motorhome is the Firestone Transforce. Most likely you will need to order them online as most stick and brick tire shops don't have them in their ordering system.
You may be able to find 17 wheels that will fit, but they are not made anymore so you have to check salvage yards, etc. And you have to make sure the bolt pattern is correct.
It's a very long read, but you can find information on
this thread
1975 American Clipper RV with Dodge 360 (photo in profile)
1998 American Clipper Fold n Roll Folding Trailer
Both born in Morgan Hill, CA to Irv Perch (Daddy of the Aristocrat trailers)