Here are a few resources that address different philosophical-anthropological aspects of your question. I haven't come across one resource that covers everything, but will checkout Chris Sunami's suggestion.
Greek (and Roman) Philosophy and Christian Revelation
Greek thought came in multiple waves: the Eastern portion of the Church (today's Orthodox Churches) had Greek as it's primarily language, and so necessarily had some intellectual borrowings from Greek Philosophy.
The second wave one can point to comes in the later Middle Ages, by way of Aquinas, who heavily use Aristotle's work. I seem to remember this being discussed in the History of Philosophy podcast, I can't remember which episode though, but my recollection is that Aristotle was mostly not well read in the West, but was read frequently in the East (where Greek was spoken), and he continued to be read after the areas that were Greek speaking became Arabic speaking after Islam came to power in those areas.
Augustine was heavily influenced by Roman writers, primarily Cicero. Most editions of his work that have preface material discuss this, and he himself includes many details of what works influenced him philosophically in his Confessions.
The challenge here is that the presence of similarities between having a patron Saint of this-or-that and having the god or goddess of this-or-that is often used by Christians who are not Catholics as a way of attacking Catholicism, without asking where it comes from, and so are often more about grinding a particular axe then a search for truth.
While similar, there is a fundamental difference, and Augustine in City of God addresses why he thinks that polytheism does not make sense. I don't recall him explicitly mentioning it, but the extension of his argument seems natural: it doesn't make sense to have gods of human inventions, because gods are supposed to precede humans, meanwhile it is natural to say that particular saints are important to such-and-such a human invention or cause, because those saints were human and therefore cared about the cause during their earthly lives.
Semi-divinity of Heros
Rightly or wrongly (I would argue rightly, but since I am Catholic I am biased), orthodox Christianity (little-o, meaning those who accept the Nicene creed) has always gone to great efforts to distinguish itself from pagan religions by stressing Jesus as not half-man-half-god, but as fully man and fully God. This is the central point of many, if not most, heresies before 1500. For a good video description of these different heresies, I would recommend the Yale course on the Middle Ages or the relevant episodes from Jim Papandrea, or any resource on this question, which theologians call "Christology."