I attend a parish which uses Greek and English in the liturgy. I am able to understand a modest amount of the Greek, and I sometimes use the service book to help, but the
service book doesn't seem to include all of the hymns they sing while people are receiving Communion. I am not chrismated and so I don't yet go up to receive, but I thought the songs were lovely. I would much appreciate it if anyone could point out a website or a listing somewhere which indicates the usual Communion hymns one might hear in a Greek Orthodox Church. Thank you very much.

Some chanters repeat the Entrance Hymns of the Day; some go back to the last 3 or 4 stichera from Orthros/Matins for that day. Some do both.
Since the Entrance Hymns (and the stichera from Orthros/Matins) vary from week to week, there are many sources where one can find them.
http://www.analogion.com comes to mind. Warning, most of this is in Greek.