I have read that Galilee was more Hellenized than other areas of Israel in the time of Jesus based on the archaeological evidence. Many of the sayings of Jesus are popular saying of Cynic philosophers, so some people (like the Jesus Seminar) wondered if Jesus might have been a Jew who had studied Cynic philosophy.
On the other hand, there is the claim that a Hebrew or Aramaic version of Matthew existed, so that might have indicated many Jews were more comfortable with Aramaic than Greek.
On the other hand, there is the claim that a Hebrew or Aramaic version of Matthew existed, so that might have indicated many Jews were more comfortable with Aramaic than Greek.