You have some choices. See this article for some of them:
http://word.mvps.org/FAQs/General/InsertSpecChars.htm.
You may also want to consider using a Greek-language keyboard in Windows. I
have used a German keyboard this way. A foreign language keyboard as a sort
of "virtual" keyboard. Go to Keyboard in Control Panel and either add or
select the language keyboard you want and then switch to it. Then you will
have all the characters of that language at your fingertips. You can then
toggle back and forth between English and Greek if you want. The only
drawback is that the "actual" keyboard --the one you are tapping with your
fingers--will still look the same, even though Windows has remapped the keys
so that, e.g., the letter p might result in a different Greek character.
You have to remember which keys on your "actual" keyboard correspond to the
characters of the keyboard for that language.
If you do all of your work in Greek, maybe you can buy an actual Greek
keyboard, but I have no idea where. But then you will have to figure out a
way to type in English. If the keyboards are connected to the computer
through a USB port (or maybe by radio, such as Blue tooth), maybe you can
swap them in and out as needed. Just a thought.