Firstly, I must point out that I am not jewish; however, I exchanged genealogical info with Jewish clubs. Jewish clubs are extremely well organised and most members are very knowledgable.
I know from information I received that the Jewish community in Corfu was well organised and about 30-35 years ago the produced various historical notes with info about various families that were active specifically in the Ionian Islands area and generally in Northern Greece.
The Jewish community in Saloniki was by far the largest in Greece with over 50,000 members (I believe there are about 10,000 today).
You can contact the Jewish Genealogical Soc of Melbourne, Australia, they may be able to give you some info. There are many Australian Jewish families from Greece here.
Also I am told, there is a very good database for Jews (privately owned?) in Hungary but I can not tell you how to access it.
The ex French President Sarkozy was also a Greek Jew, born in Saloniki.