I can do little better at this time than to quote some passages from someone who is perhaps the most important Greek theologian of our day, Metropolitan Hierotheos (Vlachos):
"It is a commonplace to declare from the start that there is a difference between philosophy and theology, since philosophy is man's invention, founded on the brain and the imagination, while theology is God's revelation to man, to his purified heart...
Ancient Greek philosophy makes a clear distinction between matter and reality. It considers reality to be a different thing from matter and the world -- all that we see and feel.
'A basic assumption of philosophy is that only the unbegotten and unchangable is immortal and real. Everything which has a beginning in time also has an end.' [here quoting Fr. John Romanides] Starting from this finding, ancient philosophy arrived at varioius conclusions which are diametrically opposed to the teaching of the Church. According to the ancient philosophers, 'creation is either a natural emanation of the essense of the one (pantheism), or a seeming or even fallen reflection of an unbegotten real world of basic ideas (idealism), or an indissoluble union of form and matter...' [again quoting Romanides]
Thus the philosophers either ended in a pantheism according to which God is identified with the world, or in an abstract idealism according to which God is a perfect, impersonal and inactive being, or else God is something evermotionless moving the ever-moving, without contact with the world.
...according to philosophy, man's liberation lies in fleeing from perishable matter and attaching himself to the unbegotten.
It can readily be seen that the god of the philosophers and philosophy is not the God of the Church, that the god of philosophy is an abstract and non-existent god and that the man of philosophy is not the same as the man of the Church.
In all these theories of the philosophers and philosophy we can see the antithesis of theology, and more generally of the Church's teaching and life, at two particular points. One is the content of the philosophers' teaching and the other is the methodology which the philosophers employ in coming to these conclusions.
All of the philosophers' views were rejected by the Fathers of the Church. In the Church we do not accept the teaching about ideas, nor the ontology of God as the philosophers describe it, not the pre-existence of the soul, nor the eternity of the world and of time, nor what is said about man's release, that the soul must leave the body, which is the soul's prison -- nor that God is the prime unmoving mover, etc.
By contrast, the holy Fathers express the Church's truth that God is not the idea of the good, as Plato said, but the personal God who was revealed to the Prophets, Apostles, and saints.
The holy Fathers also teach that love is not only a motion of man towards God, as Plato said, nor does it express the powerlessness of man who is moved towards the prime unmoving mover in order to feel completeness, but that it is a positive energy. God is not simply the unmoving mover, but He is at the same time moved towards man. He moves and is moved. And love is not a matter of man's weakness, since God Himself, Who is love and the object of love, Who moves and is moved, is also called love.
The fact that the Church rejected all these theories of the philosophers can be seen presented concisely in the Synodikon of Orthodoxy, a text which is read on the Sunday of Orthodoxy. Indeed not only were these theories rejected as heresies, but it is said explicitly and repeatedly that anyone who accepts the theories of the philosophers is anathematised by the Church. All who accept "the Platonic ideas as true" and say and accept "that matter is self-existent" are anathematized. Likewise all who accept and spread "the false and Hellenic sayings", all who assert that souls pre-exist and that all things did not come into being from naught, and have gone astray" are anathematised."
All of these brief excerpts come from a book called "The Person in the Orthodox Tradition." It is just one readily accessible book that should be read by anyone who wants to understand the relationship of Hellenic thought to Orthodox Christianity.
Because of the subject matter, it is quite "philosophical" compared to most Orthodox writings (the average Orthodox Christian is so far from the questions and issues of pagan Greek philosophy as to make these topics irrelevant), but it is a book that fills an important need.
Interestingly, the title of the first edition of this book, before it was expanded in its second edition, was "Person and Freedom," since personhood and freedom are inextricably related.
There is a somewhat different perspective expressed on the Greek Orthodox Archdiocese of America website that discusses how the tension between Hellenistic thought and Christianity was resolved.
The spread of Christianity would have been impossible without the Roman Empire that turned the Mediterranean into a big Roman lake. Christianity never took deep roots in the Semitic world but Islam did. Christianity eventually flourished in that Greco-Roman culture of the Roman Empire once a systhesis had been worked out. There were many points of contact that made that possible.