So, Luke 16... Did I mention that parables are weird? Let's just move down to verse 15.
The SAB says "That which is highly esteemed among men [love, wisdom, honesty, courage, truth, beauty, etc.] is abomination in the sight of God." I don't think that that was what Jesus was referring to in that verse. Coming right after "Ye cannot serve God and mammon," I would assume that Jesus is referring to money, but I may be biased, I'll admit.
In verses 16 and 17, Jesus talks about the law, and the SAB feels that what is being said there is a contradiction. I've always said that when you read two verses that are side by side and they seem to contradict, you're almost certainly misunderstanding them. Still, the question Must Christians follow the OT laws? points right to the heart of the matter. I've always taken the position that the answer is no, so what is Jesus saying by verse 17? I think he's saying that the OT law is important, and even if it doesn't apply to Christians living under grace, it does continue to serve a purpose. Paul talks a lot about how the Law points to our sinful nature and a need for God's grace, thus the OT law is a big part of the new covenant for Christians.
Verse 18 talks about divorce, and in some of the strongest terms you'll find in the Bible. Is divorce ever permissible? and Is it OK for a divorced woman to remarry? I ended up asking a friend who is a pastor for advice on this chapter, since there was a lot that was tricky, and his view was that much of what appears in this chapter is specifically aimed at misguided ideas that the Pharisees had about various things. One of the things that the Pharisees believed was that you could get a divorce for any reason at all. It may be because of this that Jesus speaks so strongly about divorce. Note that the verse that the SAB pulls from Deuteronomy says "because he hath found some uncleanness in her," which indicates to me that even this verse is talking about unfaithfulness. I think that Jesus is saying that if you up and divorce your wife for petty reasons, it's not really a proper divorce, and instead of divorcing because of adultery, you're really causing adultery.
The chapter ends with the famous story of the rich man and Lazarus. According to my friend that I asked for help, there may be more to this story than we're seeing on the surface. The Pharisees believed that the poor would receive comfort in the afterlife, and therefore it was better not to help them, as you would be reducing their rewards. Jesus is pointing out that by that logic, rich people such as the Pharisees must end up with punishment in the afterlife, since they had plenty of rewards just in their life in general. So this story is mainly to make a point of the Pharisees' beliefs. Note however that there is an interesting point at the end of the story: "If they hear not Moses and the prophets, neither will they be persuaded, though one rose from the dead." Very suggestive of Jesus' resurrection, isn't it?