We have no evidence to suggest that He spoke Greek, and the majority of the people in the region in which He was that He was speaking to would not have spoke Greek. He was speaking almost exclusively to Jews in the region, most of whom would have understood Aramaic, and Hebrew but not Greek. Also given the fact that the Greek language is so full of terms derived from pagan gods I find it hard to believe that He would use it. But to be fair a more accurate statement is that we have no record of Yahowsha ever speaking so much as a single Greek word.

The evidence seems to suggest that the Jews, at lest racial Jews, have clung to the Hebrew language for the Towrah. Even to this day most racial Jews will read the Towrah in Hebrew, and most synagogues will do readings in Hebrew, even if they translate it as well. From what I understand of the 1st century in Judea, based on the archaeological evidence, and other writings of the time the language spoken by most all Jews in that region was Aramaic, or Hebrew, and while the Towrah had been translated into Greek, i.e. the Septuagint, that was not used in the Judea region.

some manuscripts of the septuigent were found among the DSS, but a very small amount compared to the Hebrew manuscripts found. From my understanding, limited, it was used in other parts of the world where Jews had assimilated to the culture and language where they lived.