I cannot offer you the official Orthodox response to Calvinism (if one even exists), but I can offer you my response as an Orthodox Christian who at one time was heavily involved in Calvinism.
By the way, Luther also taught that human beings do not have free will. His treatise, On the Bondage of the Will, makes that abundantly clear.
What you referred to you in your original post is part of what Calvinists would call Total Depravity, the doctrine that Original Sin has completely ruined humankind, which is dead in sin and condemned from birth, unable to even choose to believe in Christ and do good.
To me there are good reasons for rejecting this doctrine.
1) It is contrary to ordinary common sense.
Most human beings desire the good and are subject to the law of their consciences. Many who are not Christians are nevertheless very moral and upright people.
That is not to say that their own righteousness can save them; it cannot. All human beings are sinners and separated from fellowship and communion with God. Only the grace of God in Jesus Christ can save them.
Ordinary common sense also tells us that it would be unreasonable and unjust for God to condemn people for something about which they have no choice. If I am a sinner because I am absolutely compelled to be a sinner, how can God justly condemn me?
The idea that human beings are born guilty for the sin of their remote ancestors is also contrary to common sense, the concept of justice, and the Orthodox understanding of Original Sin.
How would you feel if agents of the FBI broke into your home, threw you to the floor, then handcuffed and arrested you for a crime your grandfather committed back in 1930?
Would a reasonable person see any justice in such a thing?
How is it then that so many believe that innocent babies are born absolutely damned because of the disobedience of their extremely remote ancestors?
How is it then that some believe we were all "legally present" in Adam?
Justice is justice. If I can imagine a justice higher than God's, then I've got the wrong God.
That is clearly the case with Calvinism, which makes a kind of implacable Moloch out of the God of love.
2) Calvinism runs contrary to the plain sense of Scripture, which speaks of choices between good and evil, between serving God and serving self, and of the love of God for all mankind and His desire that we all be saved.
Though the Bible speaks of all human beings falling short of the glory of God, of our being sinners, yet it also says that human beings were created in God's image, that the Divine Word enlightens every man, that the human conscience is the lamp of God. Many persons throughout the Bible are called "righteous," and human beings, though stumbling often, are honored and respected by God for their efforts at obedience.
Look at the example of Cornelius the Roman centurion in Acts 10. He was neither a Jew nor yet a Christian, yet his alms and prayers were accepted and respected by God. Cornelius exercised his free will to pursue the kingdom of God. He was rewarded when the Lord sent St. Peter to preach the Gospel to him and he and those with him received the Holy Spirit.
The Lord did not turn His back on Cornelius and disregard His alms and prayers as "filthy rags," the products of a "totally depraved" sinner.
Don't get me wrong. I am not saying Cornelius earned his salvation in some way. No, Cornelius was saved by the grace of God. But it is apparent that he pursued God and did his part to acquire that grace which is freely available to all.
Now Calvinists would argue that the Holy Spirit chose Cornelius and that everything he did was the product of the prompting of the Spirit.
Well, read the account in Acts 10. There is nothing there about the Holy Spirit compelling Cornelius to act as he did. One must begin with Calvinist presuppositions and read them into the biblical account in order to see them.
Undoubtedly the Holy Spirit was working with Cornelius, just as He works with all those who seek the Lord; but there is nothing in Scripture anywhere to support the notion that God's Spirit forces people into faith and repentance.
It is true that human beings are "dead in trespasses and sins." But does that necessarily mean that we are utterly dead and must become Zombie-like creatures, completely controlled by God like marionettes? Can we not even choose to repent and be baptized?
I see no evidence of that in Scripture or the writings of the Church Fathers.
Human beings are dead in trespasses and sins because we are born into a world in which fellowship with God has been broken. Adam and Eve broke fellowship with God; that is Original Sin, and the primary consequence of it was death.
Human beings are dead to God, but Jesus Christ has trampled down death by death. We are able to exercise our free will to choose to believe, repent, and be baptized. In baptism we are raised from spiritual death and experience the "first resurrection," which is the new birth.
Calvinists would argue that dead people cannot choose anything because they are dead. Here I think they are applying a thoroughly wooden kind of literalism which is contrary to Scripture and reason.
Obviously people make choices between Good and Evil, between God and the devil. If those choices are not free, then human beings are merely pawns, and why worry about it at all? Just wait for God to move you to the proper square at the appropriate time and for the Judgment to find out if you were a white piece or a black.