Σιμπλζ αδδ τηε Γρεεκ λαζοθτ το ζοθρ Κεζβοαρδ λαζοθτ πρεφερενψεσ. Τηεν αδδ τηε Κεζβοαρδ Ινδιψατορ αππλετ το ονε οφ ζοθρ παλελσ ανδ θσε τηατ το σςιτη λαζοθτσ.
Simply add the Greek layout to your keyboard layouts. Then add the "Keyboard Indicator" applet to one of your panels and use that to switch between layouts. It seems to work for me.
Changing the layout via a key combination seems to be a bit flaky:
Choose "Layout options" in the Keyboard preferences dialog and find the group of options labled "Keys to change layout". You will then simply have to try the different options and see which one works for you, both on a system level and a usability level. I guess for the option that says "both alt keys" you will need two Alt keys (I have only one here). On the other hand, I definitely have to Ctrl keys, but the "Both Ctrl keys" option doesn't work for me either.
I understand that you want to avoid cluttering your panel, but my guess is that you will need some sort of indicator of the current layout or you'll find yourself constantly typing in the wrong one. Of course, your mileage may vary.