The Gospels were written some time between 70-130 CE. They were not eye witness accounts. This itself is a major strike against the historicity of Jesus, for if he were as important as the Gospels make him out to be, we'd expect someone to have written his story down sooner than that.
Historicists, those who believe that Jesus was based on an actual historical figure, claim that the Gospels were based on an oral tradition. However, if that's the case, why do they rely so heavily upon the Old Testament and provide so little original material?
The Gospels of Mark, Matthew, and Luke are so similar to each other, they're referred to as the synoptic gospels. When comparing the Gospels side by side, it's apparent that they copied from each other. Mark, being the shortest, was likely written first, since it's highly unusual for a story to get shorter rather than longer over time.
Mark was largely based upon the Old Testament. In fact, it reads as if someone went through the Old Testament, took every reference to the Messiah they could find, and combined them all together into a single narrative. The Jewish practice of combining scriptures together like this, known as midrash, was actually quite common at the time. Mark makes much more sense when viewed as a midrash than as an oral tradition that was written down.
Matthew and Luke both took the story of Mark and expanded upon it, adding additional events and sayings. It's obvious from the numerous contradictions between Matthew and Luke (for example, both give a completely different genealogy for Jesus) that they weren't aware of each other.
So if Mark, Matthew, and Luke are all ultimately derived from a single source, where did the gospel of John come from? John is quite a bit different from the synoptic gospels. In fact, it reads more like a modified gnostic gospel.
The gnostics were a group of early Christians, who some scholars believe actually predated Pauline Christianity. Their writings include such titles as the Gospel of Mary, the Gospel of Thomas, the Gospel of Truth, the Gospel of Philip, and the Gospel of Judas. Many of their ideas can be found in the Gospel of John, however John appears to have been modified to fit the synoptic Gospels more closely, making it a hybrid document.
John didn't agree with the way Jesus was portrayed in the synoptics. He didn't like that Jesus showed moments of weakness, such as when he asked that the cup be passed from him:
And he went a little farther, and fell on his face, and prayed, saying, O my Father, if it be possible, let this cup pass from me: nevertheless not as I will, but as thou wilt. (Matt. 26:39)
John's version of Jesus carries his own cross, speaks up for himself in the presence of Pilot, and never wavers when it comes time to make his sacrifice.
Then said Jesus unto Peter, Put up thy sword into the sheath: the cup which my Father hath given me, shall I not drink it? (John 18:11)
So even if the Gospel of John is largely divergent from the synoptics, that doesn't mean John was ignorant of them as he can be seen responding to them from time to time. There's no compelling evidence that any of the Gospels were based on oral tradition.
Jesus, if he had existed, would have spoken Aramaic and Hebrew, yet the writers of the Gospels didn't know Hebrew. They were all Greek speakers who quoted from the Septuagint, the Greek translation of the Old Testament. In fact, the virgin birth, not mentioned in the Gospel of Mark, is based on a mistranslation from Isaiah.
Therefore the Lord Himself shall give you a sign; Behold, a virgin shall conceive, and bear a son, and shall call his name Immanuel. (Isaiah 7:14)
The word translated above as "virgin" actually means "young woman" in the original Hebrew, but Matthew didn't know that:
Now all this was done, that it might be fulfilled which was spoken of the Lord by the prophet, saying, Behold, a virgin shall be with child, and shall bring forth a son, and they shall call his name Emmanuel, which being interpreted is, God with us. (Matthew 1:22-23)