The Orthodox view is expressed in this note in The Orthodox Study Bible:

‘Mankind’s strong propensity to commit sin reveals that in the Fall, the image of God in man (Gn 1:26, 27) is also fallen. However, the ancient Fathers emphasize that the divine image in man has not been totally corrupted or obliterated. Human nature remains inherently good after the Fall; mankind is not totally depraved. People are still capable of doing good, although bondage to death and the influences of the devil can dull their perception of what is good and lead them into all kinds of evil.’

This I find a bit confusing.  In its negations, it seems to oppose itself to the supposed Reformed doctrine of ‘total depravity.  But Reformed theology does not teach that ‘the divine image in man has…been totally corrupted or obliterated’.  It teaches, rather that it has been defaced, but not destroyed.

Turning to Timothy Ware’s exposition of Orthodox teaching on the fall, depravity and the distortion of the divine image in man:

On the fall:

‘Orthodoxy, holding as it does a less exalted idea of the human state before the fall, is also less severe than the west in its view of the consequences of the fall. Adam fell, not from a great height of knowledge and perfection, but from a state of undeveloped simplicity; hence he is not to be judged too harshly for his error. Certainly, as a result of the fall the human mind became so darkened, and human will-power was so impaired, that humans could no longer hope to attain to the likeness of God.’

On depravity:

‘Orthodox, however, do not hold that the fall deprived humanity entirely of God’s grace, though they would say that after the fall grace acts on humanity from the outside, not from within. Orthodox do not say, as Calvin said, that humans after the fall were utterly depraved and incapable of good desires. They cannot agree with Augustine, when he writes that humans are under “a harsh necessity” of committing sin, and that “human nature was overcome by the fault into which it fell, and so came to lack freedom”.’

On the distortion of the image of God by sin:

‘The image of God is distorted by sin, but never destroyed; in the words of a hymn sung by Orthodox at the Funeral Service: ‘I am the image of Your inexpressible glory, even though I bear the wounds of sin.’

On ‘free will’:

‘And because we still retain the image of God, we still retain free will, although sin restricts its scope. Even after the fall, God ‘takes not away from humans the power to will – to will to obey or not to obey Him’. Faithful to the idea of synergy, Orthodoxy repudiates any interpretation of the fall which allows no room for human freedom.’

However, Ware does not find the differences between East and West on this points to be absolute:

‘Although Orthodox maintain that humans after the fall still possessed free will and were still capable of good actions, yet they certainly agree with the west in believing that human sin had set up between humanity and God a barrier which humanity by its own efforts could never break down. Sin blocked the path to union with God. Since we could not come to God, He came to us.’

The Orthodox Church: An Introduction to Eastern Christianity, ch. 11 (1997)

I’m not sure that I detect anything distinctively ‘Eastern’ about this teaching.  Certainly, it differs from Reformed theology, but not from Arminian or semi-Pelagian doctrine on sin and depravity.