For error 7302 in particular, I discovered, in my registry, when looking for OraOLEDB.Oracle that the InprocServer32 location was wrong.
If that's the case, or you can't find that string in the registry, then you'll have to install or re-register the component.
I had to delete the key from the GUID level, and then find the ProgID (OraOLEDB.Oracle) key, and delete that too. (The ProgID links to the CLSID as a pair).
Then I re-registered OraOLEDB.Oracle by calling regsvr32.exe on ORAOLEDB*.dll.
Just re-registering alone didn't solve the problem, I had to delete the registry keys to make it point to the correct location. Alternatively, hack the InprocServer32 location.
Now I have error 7308, about single threaded apartments; rolling on!