Will a divorce judgment obtained in Israel from the Greek Orthodox Church court in Israel be sufficient for me to remarry in the United States, where I live, without having to get a civil divorce there?

Firstly, the Israeli divorce judgment should bear the 'Apostille seal' to show that it was a genuine document. Both the United States and Israel recognize each other’s documents as being genuine if they bear this seal, according to a Hague Convention on the issue. Secondly, assuming that the divorce judgment was given by an Israeli court with jurisdiction, according to law, and that it is final (i.e. no longer appealable), then, because Israel and the United States recognise one another's judgments, it should be recognisable in the United States. However, whether it would be sufficient for you to be married there, without the need for a civil divorce, or a judicial process of recognition, depends upon the laws of the state where you intend to marry, and you would be advised to check this out in the state where you wish to remarry.