STDs were definitely known in ancient Roman times. You can find the description of what is assumed to be Gonorrhea in the works of Aretaeus, who lived in the 1st century CE. Here's a small excerpt cited in another book.

The origin of Syphilis is still under dispute. The majority opinion seems to be that Syphilis was imported from the Americas to Europe; a minority opinion is that it existed in Europe before, but went unrecognized. In any case, this means that Romans would at least not have recognized it as a separate STI.

As an aside, I think you're overestimating the prevalence of sexual orgies in ancient Rome.

Herpes and gonorrhea were well known to the Greeks and Romans. There's a good thread here on the subject.