What a great subject this is ... one of the most intensive and productive areas of recent Islamic scholarship has been to analyze the Qur'an in terms of the Christian texts it assumes that its audience knows and is familiar with.
The Christianity that prevailed in Syria/Iraq/Jordan and Arabian regions was very different than what we now think of as Christianity, and the orthodox doctrines of Christology penetrated very slowly and partially into the area. What's more, even the gospels did not get translated into Syriac until extremely late, and they did not get translated into Arabic until later still. Before that point, Syriac Christianity used a sort of mix of informal different texts, and the "Gospels" used in that region were primarily something called the Dietessaron, a sort of synthesized Gospel that was written early. Modern scholars believe that the Qur'an's discussion of Christianity is dependent on the Diatessaron, and that when the Qur'an speaks of the "Injil," it is probably talking about the Diatessaron.
http://en.wikipedia.org/wiki/DiatessaronThe other gospel source that the Qur'an draws on is the apocryphal Gospel of Thomas, not only for the infancy story, but for other stories like the "clay birds" story. Orthodox Christianity later became embarrassed by these stories, but the Qur'an reflects a time period when they were taken very seriously (likewise the Seven Sleepers of Ephesus).
It is an amazing fact that the Bible was not translated into Arabic until something like the year 1000 AD! So when Arabs were Christianized (and the Qur'an assumes its audience is familiar with Christianity and Christian texts), they would have had to access/read/recite the scripture through Syriac or Palestinian Aramaic. This is why the Qur'an's discussion of Christianity, and its religious terminology generally, seems to reflect archaic Syriac/Palestinian Christianity -- which in turn was much more Judaic in character before the Nicene and Chalcedonian reforms slowly brought it to heel over centuries.
There is a lot to be said for Islam having begun as a sort of older pre-Nicene Christianity that existed on the Syriac/Arabic fringe, and which reflects the older Judaic style of Christianity that was dominant in the East until it was replaced by Hellenistic Christian trinitarian theology. Basically it is Arabic preaching of ancient Eastern Christianity, in which Jesus is divine because of his obedience to God (which is how we are all saved), not because of his inherent nature and his crucifixion. The Qur'an does not seem to have envisioned itself as a replacement for older scriptures so much as a *commentary* on older scriptures, which corrects the scriptural misunderstandings of the Jews and the trinitarian Christians. Only later was the Qur'an divorced from its Christian context and set by Muslim tradition into the "pagan Hijaz," which IMO is an almost entirely mythical story.
Topic: Early Christianity and the Islamic Jesus