... In the first volume of this series, we argued that when Galatians uses the phrase "works of Law," Paul primarily had in mind those parts of the Jewish Law that distinguished Jew from Gentile.  In Galatians, circumcision in particular was the key issue under discussion when he said, "no one will be justified by the works of the law" (2:16, NRSV). The argument of Romans is more general, and certainly Paul did not think anyone could earn God's favor, but the key subject was still whether a Jew had any advantage over a non-Jew in being right with God. The underlying issue is not "Can you be good enough for God to accept you?" It is "Is there something about being a Jew that automatically makes you right with God?"
So when Paul says he is not under Law (e.g., 1 Cor. 9:20) and that right standing with God does not come by "works of Law" (e.g., Rom. 3:28), he primarily has things like circumcision, Jewish food and purity laws, and Sabbath laws in mind. Yes, as part of that argument he makes general statements about the impossibility of earning a right standing with God (e.g., Rom. 4:4-5; 9:32). But it is a supporting point, not the main one. When Paul distances believers from the Law, he primarily has the Jew-specific aspects of the Jewish Law in view, the boundary type laws that most distinguished Jew from Gentile.
What is confusing is that Paul also talks about the Law with a very different content in view. Sometimes he has a certain "core law" in view that is universal and timeless. When Romans 2:14 talks about Gentiles who "do by nature things required by the law," it cannot refer to Jew-specific elements. Gentiles by definition do not do such things. Paul can only have a certain universal, "moral" core in mind, if you would. It is this part of the Jewish Law that Paul has in mind in Romans 6-8.
The key to understanding Romans 6-8 is to understand the clear "before and after" he presents repeatedly throughout the section...
 Paul: Messenger of Grace