There are multiple ways of interpreting the question because 'angel', or rather ἄγγελος, is a job description rather than a class of supernatural being. It simply means 'messengers'.

Human messengers are a commonplace thing in classical and hellenistic Greece, and they're standardly called ἄγγελοι. The word is much earlier than any likely direct influence from Israel or the Jewish diaspora.

There are a couple of divine messengers that appear in Greek literature prior to the Roman era: in particular, the divinities Iris and Hermes, who both perform this function in the Homeric epics. Hermes is a god associated with guidance between the upper and lower worlds; Iris, with rainbows. They bear messages both to mortals and to other divinities, usually at the behest of Zeus. Again, this is much earlier than any likely Jewish influence.

The distinction between English 'messenger' and 'angel' arises as a product of translation. In biblical texts, when Greek ἄγγελος or Hebrew malakh is used of mortal messengers, they typically get translated as 'messenger'; when used of supernatural beings sent by God, they get translated as 'angel'. This difference is one of context, not a distinction in the ancient languages.

The popular image of angels as human figures with bird wings is a relatively late development, dating to late antiquity. Prior to that, Judaeo-Christian angels look like humans, sometimes distinguished by their clothing. I suppose it's possible that the 'winged human' image is partly influenced by Greek pictorial depictions of souls of the dead, which are often shown as a miniature of the dead person fluttering about on bird wings.

It's also possible that there's some influence from other kinds of supernatural entities in Jewish tradition, such as Cherubim, Seraphim, and Ophanim. In the Hebrew Bible these are separate kinds of winged non-human supernatural entities: they are never referred to as malakhim 'messengers', and divine malakhim are consistently humanoid. But they do sometimes get conflated together in Talmudic times. By the 12th century they are explicitly treated as all belonging to a superset of 'angels', in Maimonides' Mishneh Torah, Foundations of the Torah 2. This body of evidence is rather late to serve as an explanation for 4th century winged angels, though.

Anyway, winged angels belong to late antiquity and later, as I said, not to the Hellenistic period.

I know of no books to recommend on Hellenistic angels, because in the Greek world ἄγγελος is just a common-or-garden job title, not a category of supernatural entity. It may be that you have something more specific in mind, though.