I went to FontBook and validated all fonts (select all; validate fonts). Then I trashed the fonts that had serious errors (red circle). Afterwards, I restarted the computer with Secure Boot. After logging in, I restarted the computer normally. After OS X loaded I opened a Word document. I still have the same problems with the special characters. I should add that I temporily whiped out the all my preferences to make sure a preference did not cause the problem.
Can you create documents with Greek letters in other applications, such as TextEdit?