Yeah...an orgy isn't a sex party. Like, at all. They're not even Roman. Ὄργια is the Greek word roughly corresponding to Latin's sacra. The word means "rites, rituals," particularly secret ones, and is specifically used to describe the rites of mystery cults--Attic writers like to use it of the mystery cult at Eleusis, but more properly the word describes Bacchic rituals. Bacchic rituals involved ritual frenzy and wildness, and were particularly associated with violence--Orpheus was torn apart by Maenads, and Euripides has Pentheus torn to pieces by Bacchic revelers, including his own mother who, in a state of frenzy, not only doesn't recognize her own son but even brings his head triumphantly to Cadmus. The Romans considered ὄργια a peculiarly Greek form of ritual--Petronius' line in Book Three, "Itala per Graios orgia ferre choros," "[I enter as a priest] to bring Italian rites through Greek choruses" is supposed to be distinctly ironic, since not only are there no Italian orgies, but choral poetry is a form associated with Dionysiac worship in the first place. Indeed, in 186 the Romans attempted to outlaw Bacchic ritual entirely. Mystery cults were often the subject of a lot of rumors, for obvious reasons. The Eleusinian Mysteries, for example, are among the most speculated-about subjects in our Greek corpus, and Minucius Felix famously quoted Fronto as claiming that the early Christians (whom many Romans thought of as just another mystery cult) engaged in wild, debauched rituals in the catacombs, including incest and human sacrifice. Many Bacchic rituals were particularly associated with women, who were allowed to participate freely in general--the Maenads and other ecstatic groups were exclusive to women. It's perhaps not surprising that orgiastic cults were often associated by those not included in them with general weirdness, including sexual debauchery. Christian writers condemned the debauchery, idolatry, and general ungodliness of the pagans throughout the Roman state, including making reference to orgiastic cults. But were ὄργια wild sex parties? No, that's rubbish.

Now, could a good time be had in the city? Sure. Erotic imagery and literature is all over the place, and we've got things like the brothels preserved at Pompeii--in many ways the approach to sex in antiquity was very different from ours (although it could also be a lot pruder, and frequently was, at least openly and officially). But when people like Suetonius and Tacitus go out of their way to point out the debauchery and sexual excess of people like Tiberius it should not be taken as indicative of Roman society as a whole. Suetonius makes note of Tiberius' sexual weirdness because he finds it weird--he even fucking says so, repeatedly. The Romans weren't having giant sex parties all the time, that's an absurd idea and one for which we not only have no evidence, but have all kinds of literary evidence that such an idea was repugnant to most of society and very much considered abnormal. Some Romans might have been doing such things, but that means nothing for society as a whole--sexual deviants exist in any society