The idea that the Greeks are Slavs is a bit of a
(••) ( ••)>⌐■-■ (⌐■_■)
Trojan Horse.
The following paper:
The genetic composition of the inhabitants of Greece
Indicates that the Greeks of today are quite distinct from specific 'Slavic" populations.
A key quote is:
"The estimated genetic distances between the inhabitants of Bulgaria and the four Mediterranean countries studied (Turkey, Greece, Italy and France) indicate that: The genetic composition of the inhabitants of Bulgaria is closer to that of the inhabitants first of Italy, next of Turkey, and then France, whereas the greatest genetic distance was found between the inhabitants of Greece and Bulgaria."
The way this question is phrased places Greek as a race rather than a language and culture.
The racial definition of Greek doesnt really exist as far as I know so you have to ask were the Minoans the only real Greeks? What about the Mycenaeans/Achaeans? Were the Aeolians and Ionians Greek? Or what about the Dorians that came from Macedonia and Epirus, destroyed Mycenae and created city states like Sparta? What about a Scythian, Persian or any slave that had a Greek child? When we get to the early and late Roman rule when the Latin speaker and Greek speakers started to significantly intermix are they Latins or Greeks now? Were the Pontians not Greek even if numerous Doric and Ionian Greeks were joining Mithridates? What about all the viking groups that came to live in Constantinople?
It doesnt really matter what invasion it was the Gothic invasions, Hunnic invasions, Slavic invasions, Turkic invasion etc. The Greek language and culture never disappeared as did the Greek populace and there is no such thing as a "pure" Greek or "pure" anything when it comes to race as many people with their racist rhetoric claim.
Anyway the Slavs are probably the most significant group after the Latins to become Greeks and being Greek just like being Latin or Slavic means adopting the language and culture of that group.
The question itself is wrong. Ethnicity is not an objective fixed category, it is a fluid concept agreed upon by members of the community and reified by sets of symbols and cultural behaviors. To say that the Greeks are "really" Slavic, or that the Slavs are "really" Illyrian or something entirely misunderstands the nature of ethnicity.
That being said, the Slavic migrations (and other events) did have an impact that the post-independence Greek government has worked hard at erasing. Particularly in terms of place names, there has been a lot of effort to "Hellenize" the Greek landscape by replacing Slavic, Albanian, Turkish and other names with Greek ones. This is a somewhat unwieldy database of these name changes.