It is not so important really to know which language Yeshua actually spoke, but it is profitable to be able say with certainty which He spoke if only to better understand the background to the New Testament Scriptures. These same Scriptures actually provide the weight of evidences needed to show the language that Yeshua spoke.
A little history will help to lay the foundation of this study:
Before the Babylonian captivity (586 B.C.), Hebrew - lit. Y'hudit (Jewish) 2Ki. 18:26 - was the language of the Jews (also known as Hebrews). The Law was written in Hebrew, the Temple services were conducted in Hebrew and the people spoke Hebrew. However, during the seventy years of captivity the people learnt a new language -
Aramaic
(an eastern dialect of Aramaic later referred to as Hebrew, or the language of the Hebrews). When they returned under Zerubbabel, Ezra and Nehemiah, they had forgotten their mother tongue and now needed the
Law explained to them as they did not understand the Hebrew that the Law was written in.
When Alexander the Great conquered the region, he introduced Greek as the official language; later the Romans came and brought with them Latin. So by the time of Yeshua there were four major languages in use: Eastern Aramaic, (also known as Hebrew or the language of the Hebrews) which was the vernacular (common language); Hebrew, which the Law was written in; Greek, (Kione - common Greek as opposed to classical Greek) which was the official language for governmental purposes and Latin, which was the language of the Roman Legions.
To further show that Yeshua spoke Aramaic rather than the pure Hebrew of the Law, we need only to examine the New Testament Scriptures themselves. There are several verses scattered throughout the New Testament that quote the words of the speaker directly, then give a translation so that the (Greek) reader would understand what was originally said. Using these verses it will be readily apparent what the spoken language was of the time and therefore the language that Jesus spoke (the first two verses actually quote Yeshua). It should be noted that the Greek word translated 'Hebrew' (Ebraios) literally means the language of the Hebrews [Bullinger - the Hebrew Aramaen or Syro Chaldaic; Strongs - Hebraistically or in the Jewish (Chaldee) language:-in the Hebrew (tongue)] which some modern translations have correctly rendered 'Aramaic' or 'Jewish language' (New Century Version). NB. the terms Chaldee, Aramaen and Aramaic are for all intents and purposes interchangeable.
Taking the child by the hand, he said to her, "Talitha cumi;" which means, being interpreted, "Girl, I tell you, get up."
Mk. 5:41
At the ninth hour Yeshua cried with a loud voice, saying, "Eloi, Eloi, lama sabachthani?" which is, being interpreted, "My God, my God, why have you forsaken me?"
Mk. 15:34 (Mt. 27:46)
Now in Jerusalem by the sheep gate, there is a pool, which is called in Hebrew, "Bethesda," having five porches.
Jn. 5:2
When Pilate therefore heard these words, he brought Yeshua out, and sat down on the judgment seat at a place called "The Pavement," but in Hebrew, "Gabbatha."
He went out, bearing his cross, to the place called "The Place of a Skull," which is called in Hebrew, "Golgotha,"
Jn. 19:13,17
Yeshua said to her, "Mary."
She turned and said to him, "Rhabbouni!" which is to say, "Teacher!"
Jn. 20:16
Referring to any Lexicon of the New Testament reveals that all of the above 'translated' words are Aramaic (some like 'cumi' are both Hebrew and Aramaic).
There are quite a few names of Aramaic origin that are 'translated', i.e. Cephas, Tabitha, Thomas; there is also the saying 'maranatha' (1 Cor. 16:22) which again is Aramaic; as is the term 'Abba' (now in use in modern Hebrew).
He said, "Abba, Father, all things are possible to you. Please remove this cup from me. However, not what I desire, but what you desire."
Mk. 14:36 (also used in Rom. 8:15; Gal. 4:6)
There are some that have tried to show that the language of the common people, and therefore Yeshua, was Hebrew. They use the writings of early Christian writers who refer to documents published in the 'Hebrew tongue', or 'for the Hebrews in their own tongue'. However as already seen the 'tongue of the Hebrews' or 'Hebrew' as used in the New Testament is the Eastern dialect of Aramaic.
They also point to documents found at Masada, and the sectarian scrolls and commentries on the Biblical scrolls contained within the Dead Sea Scrolls, written in Hebrew (as in the Law) to prove that the common language was Hebrew; actually it only proves that Hebrew was the common language of the Essenes, a group of extremist and exclusive religious Jews - who tried to cling to as pure an existence as possible - language probably included; whose home was the area where the scrolls were found and who committed suicide en masse when surrounded by the Roman Legions at Masada.
They also point to letters written in Hebrew at the time of the Bar-Cochba Revolt in A.D. 135. Again, these were extremists and not representative of the common people of 105 years previous (the time that Yeshua began His ministry).
It is worth pointing out that the very name 'Bar-Cochba' ('Son of the Star') - a messianic title that Rabbi Akiva gave to him in supposed fulfillment of Bamidbar / Numbers 24:17 - is itself Aramaic! The Hebrew word for 'son' is 'ben' not 'bar' and for 'star' is 'cochab' not 'cochba' (the usage of the word 'bar' has stuck until this day amongst Jews with the term 'Bar-Mitzvah' - 'son of the commandment').
Yeshua probably also had a good command of Greek and possibly some Latin, as to Biblical Hebrew - well He did read from the prophet Yesha`yahu / Isaiah (Lk. 4:17-20).
In conclusion then, although the evidence in the New Testament overwhelmingly supports Aramaic as the vernacular, it is not so important so as to cause division within the Body: God is much more interested in the language of the heart than the loudness of one's voice.