Hippolytus: The Refutation of All Heresies
The Docetists, like most Gnostics (though Hippolytus attributes their beliefs to the Sophists) believe that the flesh is evil and that only the spirit matters. Jesus was not a real person, he was rather just the appearance of one "[Jesus] contracted Himself--as it were a very great flash in a very small body, nay, rather as a ray of vision condensed beneath the eyelids."
Monoimus argues (perhaps tied to his name?) that all things in existence are one whole--man is the universe. All things are united to each other, and the purpose of the Son of man is to reunite all creation and make us aware of our oneness. (It's note really as Eastern sounding as I'm making it, but it's close.) This system is taken from Pythagoras, as we see in its obsession with math.
Tatian gets a nod here, as a student of Justin Martyr who went astray. The very brief reference suggests that maybe Tatian isn't quite as bad as the other heretics listed.
Hermogenes latches on to Socrates that God created using pre-existing material. The creation act is an eternal relationship, wherein God is always creating and matter is always being created. God is in this sense an eternal organizer, more than a Creator. Much of what Hermogenes teaches is pretty close to orthodoxy, for whatever that's worth.
The Quartodecimians (with their great name and all) hold "that Easter should be kept on the fourteenth day of the first month" [hence, the footnote tells us, their name]. They of course ignore the the Jewish calendar and the practice of Passover. "In other respects, however, these consent to all the traditions delivered to the church by the Apostles."
The Montanists, however, don't get off so easily. They hold to the doctrine of continuing inspiration of both prophets and Scripture.
And being in possession of an infinite number of their books, [they] are overrun with delusion; and they do not judge whatever statements are made by them according to the criterion of reason; nor do they give heed unto those who are competent to decide; but they are heedlessly swept onwards, by the reliance which they place on these impostors. And they allege that they have learned something more through these, than from law, and prophets, and the Gospels. But they magnify these wretched women above the apostles and every gift of grace, so that some of them presume to assert that there is in them something superior to Christ.And while they are orthodox in much of their doctrine, they end up being weird in their practice (either extremely ascetic or extremely permissive, depending on the sect in question). Hippolytus will get back to these.
The Encratites likewise teach something of orthodoxy, "in respect, however, of their mode of life, they pass their days inflated with pride." They restrain from meat and drink only water and don't marry and end up looking more like the Cynics than like Christians. In doing so, they set a standard that is contrary to the vision of the Christian life laid out by the Apostle Paul. "This voice, then, of the blessed Paul is sufficient for the refutation of those who live in this manner, and plume themselves on being just."