What is the Eastern-Orthodox interpetation of Romans 3:10-20? In his book, "On the Bondage of the Will", Martin Luther cites St. Paul in section 151, to back his view that free-will is actually in bondage, specifically Romans 3:10-20, how do Eastern-Orthodox interpret these passages?
I've translated prof. Lopukhin's interpretation of these verses for you:

for 10-18:
Accusations made by the Apostle are in agreement with those made by Jewish prophets about them. First he cites Psalms 13:1–3, 5:10, 139:3, 9:28, then books of Proverbs and Isaiah (1:16 and 59:7-8 respectively), then Psalm 35:2 again. It should be noted that the Apostle speaks of human corruption in wide terms (10-12) and then makes an accent on two specific instances - a corruption in words (13-14) and corruption in deeds (15-17). He concludes that the source of the corruption is a missing fear of the God (18).
for 19-20:
Jews could've argued with the Apostle that cited writing are related to heathens and not people of Israel (like Ps. 13). The Apostle counter that books of Old Testament are written for Jews, not for heathens. It is clear that book authors wanted to warn people of Israel, their compatriots, about God's judgement for their sins, in which they became akin to heathens. It could be, in Jews the Law foresaw the beginnings of sins that were present in heathens. &quot;The whole world&quot; - a whole humanity, both Jews and heathens - &quot;held accountable to God&quot;, that is is a subject for God's judgement, &quot;by the works of the law&quot;. Under this term the Apostle means not only deeds of rite, but also inner acts of human's will. A Jew wanted to obey all the testaments of Moses' law by his own, his own spiritual work. He wanted to exonerate himself by his own labor. The Apostle sees such ambition as unreachable - &quot;no one will be declared righteous&quot;, not a single person, as we are weak and powerless, and can not fulfill the Law in its entirety. So, the only thing that the Law gives Jews is understanding of the sad fact that it is impossible to get out of the sins abyss by their own. The Apostle speaks of that more in 8:7-11.

Hope that helps.