Greek and Aramaic are not related and we know what they look like. The Medrash is peppered with Greek and Latin but not so much the Talmudim.
The Mishna is Lashon Hakodesh because it is Torah. I have seen, though, that in Eretz Yisroel they spoke Lashon Hakodesh and purposely used Aramaic for these things. However, the examples in Eiruvin suggest that they spoke Aramaic. Perhaps it depends on the period.