The Literal Interpretation of the Sermon on the Mount

How should the words of Jesus be taken? Literally? Figuratively? Somewhere in between? Many Christians have been confused by the strangeness of many of Jesus' commands, by the apparent extremism that they seem to promote.
The words of Jesus as we have them recorded for us in the four Gospels have been interpreted by everyone from Catholics, to Protestants to Anabaptists and everyone seems to come away with a different sense. Is there a way through the morass of opinion on this subject?
If Jesus is truly the Captain of our Ship then surely it is of the utmost importance that we be certain not only of the actual words of the Gospels, but also of the correct interpretation.
Christians are divided on whether it is possible, but here we have not only one but three eminent turn-of-the-century Christians scholars taking this subject head on. They take for their case the famous (or is that infamous?) Sermon on the Mount?