You may have difficulty finding that information, as I'm not sure there is a standard definition of "expat" across the various countries. If Greece does a census, you may be able to find the numbers of Greek residents of various nationalities. Not all countries count those expats who have taken local nationality as expats any more and they may or may not ask that question when they do a national census. But in any event, try locating a website for whatever government office in Greece conducts their census.

The other option is to contact the embassies/consulates in Greece of the various countries you're interested in. Most consulates maintain some sort of estimate of the numbers of their countrymen they are responsible for. But unless people are required to register with their home consulates (as I'm told the Austrians must do), these are merely guesstimates.

With the freedom of mobility now possible under the EU, many EU nationals move to other countries without registering anywhere, so it could be tricky determining numbers for other European countries.