Do eliminated diseases like polio, smallpox etc still exist in locations they have been eliminated from or in the wild or did we just make them go extinct like the dodo?
Whether a disease can be eradicated or not depends on its reservoir. To be eliminated it needs to be eliminated in all places and organisms it can thrive in and spread from. This makes diseases like rabies for example hard to eradicate altogether because it can exist and spread in many different animal species.
Polio and smallpox however both have no non-human reservoir, which makes it possible to eradicate them. There is no "in the wild" for them to persist in because humans are "the wild" for them. So smallpox the disease has indeed been made extinct like the dodo; polio we're not quite there yet but we seem to be close.
I said "smallpox the disease" because "smallpox the virus" still exists in two laboratories in the US and Russia.
Polio, as I said, isn't an "eliminated disease" yet (as of May 2017), but since you mentioned it, the main places it persists now are Afghanistan and Pakistan.