Craig Blomberg has written extensively on the historical reliability of the Gospels.  In the relevant article in the Dictionary of Jesus and the Gospels, he identifies a number of factors that support the probability that the Gospels faithfully preserve the oral traditions on which they are based.

1. Jesus was perceived by his followers as one who proclaimed God’s Word in a way which demanded careful retelling.

2. Over ninety percent of his teachings has poetic elements which would have made them easy to memorize.

3. The almost universal method of education in antiquity, and especially in Israel, was rote memorization, which enabled people accurately to recount quantities of material far greater than all of the Gospels put together.

4. Oral story-telling often permitted a wide range of freedom in selecting and describing details but required fixed points of a narrative to be preserved unchanged.

5. Written notes and a kind of shorthand were often privately kept by rabbis and their disciples, despite a publicly stated preference for oral tradition.

6. The lack of teachings ascribed to Jesus about later church controversies (e.g., circumcision, speaking in tongues) suggests that the disciples did not freely invent material and read it back onto the lips of Jesus.

7. The degree to which Jesus emphasized his imminent return, that is, to the exclusion of envisioning the establishment of an ongoing community of followers, has been exaggerated. Hence, the claim that the disciples would have had no interest in preserving the Gospel tradition until the second generation of Christianity is doubtful.

The Gospel writers themselves insist that they used oral tradition in compiling their records of the life and teaching of Jesus Christ (see, for examples, Lk 1:1-14).  Mark Roberts concludes his discussion of the oral sources of the Gospels with the following summary points (emphases added):-

1. The first storytellers were eyewitnesses, including those who had followed Jesus closely during his earthly ministry.

2. The sayings and stories of Jesus were passed down in public settings, where errors or egregious additions could and would have been corrected.

3. Oral cultures allow for a measure of freedom in the telling and retelling of stories, but they also guarantee the essential trustworthiness of the transmission process.

4. Some, if not many, of the traditions about Jesus were passed on in forms that made them especially easy to remember and recount accurately.

5. The early Christians, as products of an oral culture, were adept at hearing, remembering, and passing on stories accurately.

6. Some of the early Christians may even have been trained by their Jewish teachers to remember the sayings of their masters with extraordinary precision.

7. Given what the early Christians believed about Jesus, they were highly motivated to pass on oral traditions about him accurately.

8. Given what the early Christians believed about Jesus’s teachings, even His words, they were highly motivated to pass them on carefully.

9. Accuracy and care do not translate into verbatim transmission, however, especially when translation from Aramaic to Greek is involved.

10. The demand for verbatim transmission is anachronistic, and is often used as a straw man to discount the basic reliability of the gospels.

11. None of what I’ve just described depends upon the help of the Holy Spirit. When you add in this spiritual element, you can have even greater confidence in the oral memory of the early church, but this is a theological more than a historical point. A non-Christian can still have confidence in the general reliability of the process by which the words and deeds of Jesus were passed down.