Given Jesus' roots in Nazareth, and given his early ministry among common folk in Galilee, it seems most likely that he usually employed Aramaic in his teaching, and this is confirmed by the data of the Gospels. But, given the likelihood that Jesus knew Hebrew as a second language, and given his frequent debates with Jewish religious teachers, and given the movement of his ministry to Judea, where Hebrew was more common, I am convinced that Jesus did teach in Hebrew at times.This sounds about right to me.
Earlier installments noted here.