On his blog, entitled גֵּר־וְתוֹשָׁב (ger vatoshav), David Miller has written a series of six fascinating posts about the translation and semantic range of the Greek word Ἰουδαῖος Ioudaios. In the series he offers helpful surveys and critiques of important scholars who have written on this issue, including Mason, Cohen, and Esler. In the sixth post he offers some tentative conclusions. At the bottom of that post are all the links to the previous five post, all of which are great reads.
Thanks David for sharing this fascinating series of post with the inhabitants of the interwebs!