The language that the children of Israel spoke in the days of the Old Testament was Hebrew. However in 586 B.C. they went into the Babylonian captivity where Aramaic was main spoken language. Aramaic, a sister language to Hebrew, began to spoken by the Jews from the Babylonian captivity onward.
When Jesus came into the world the Greek language was spoken in all parts of the Roman Empire. There were however, both local and regional dialects. It seems the Jewish people in Israel Jesus' day continued to speak Aramaic.
Greek Was The International Language
Greek became the international language through the conquests of Alexander the Great (330 B.C.). We know that Jesus was able to speak Greek because several of His conversations could have only taken place in the Greek language. This includes the account of His speaking to the woman with the demon-possessed child (Matthew 14) as well as His conversations with Pontius Pilate.
Aramaic Was Also Spoken
Jesus also spoke Aramaic in His public ministry. We have several recorded sayings of Jesus in the Gospels that are transliterated from Aramaic to Greek. These include the words He uttered at the raising of Jairus' daughter.
He took her by the hand and said to her, "Talitha koum!" (which means, "Little girl, I say to you, get up!") (Mark 5:41).
Here Mark translates the Aramaic phrase for his readers. Other Aramaic words found in the New Testament are abba, and ephphatha.
Hebrew May Have Been Spoken
There is the possibility that Jesus spoke in Hebrew at times. Some people argue that Hebrew was actually the main language that Jesus spoke but this is a minority view.
Latin Was Spoken Only By The Elite
Although Latin was the official language of the Roman Empire it was not spoken by the masses. Only the aristocracy would converse in Latin.
The Sign Over The Cross Was In Three Languages
The sign over the cross of Jesus illustrates the fact of the many languages spoken at that time.
Pilate had a notice prepared and fastened to the cross. It read: JESUS OF NAZARETH, THE KING OF THE JEWS. Many of the Jews read this sign, for the place where Jesus was crucified was near the city, and the sign was written in Aramaic, Latin and Greek (John 19:19,20).
Summary
The world in which Jesus came had an international language, Greek. Jesus obviously spoke Greek. There are certain occasions that the New Testament records for us where Jesus would have had to have spoken Greek - to the Syro-Phoenecian woman as well as to Pontius Pilate. On other occasions He probably spoke Aramaic. It is possible that He spoke Hebrew on occasion. We know that He could read Hebrew.