Our quick answer is that Jesus primarily spoke Hebrew (especially for teaching [all rabbinic parables are in Hebrew], prayer, and conversing with fellow Jews from the land of Israel), he almost certainly knew Aramaic (which he would have spoken in conversation with local Gentiles and diaspora Jews from the east), and he probably knew a little Greek as well.
The following two JP articles by Shmuel Safrai are essential reading on the question of Jesus’ language(s): “Spoken Languages in the Time of Jesus” and “Literary Languages in the Time of Jesus.”
Equally important for the language question is be the Jerusalem School of Synoptic Research’s monograph: The Language Environment of First-Century Judaea: Jerusalem Studies in the Synoptic Gospels, Volume 2 (ed. R. Steven Notley and Randall Buth; Leiden: Brill, 2014).
Note, too, the extremely valuable article by the Hebrew University’s Steven Fassberg: Steven E. Fassberg, “Which Semitic Language Did Jesus and Other Contemporary Jews Speak?” Catholic Biblical Quarterly 74 [April 2012]: 263-280.
