I'm a Reformed Presbyterian, so keep that in mind per my answer.
Jesus said he came to fulfill the law, to bring it to its purpose. Everything in the Old Law pointed towards Christ, kept the people of Israel separate from the world, taught them certain things about the way Christ was to be (not always obvious what each law taught). A key thing these laws taught the people was the curse enacted at the Fall, which was enacted against man through the dust of the ground. Even man's own flesh (made of dust) caused him to be unclean. Since God is clean, He desires his people to be. So the Law taught primarily that we are unclean people, and must be cleansed.
For example, animals without "shoes" (hooves) were unclean because they had nothing to separate them from the unclean ground. If you came into contact with a dead body, it had the same effect. Think of how you would see the world if everything you did was shaped by this constant reminder? Also, remember that Moses at the burning bush was told to remove his shoes: the ground was clean because God was there, Moses had no need of something to keep him from the uncleanness.
Jesus is the fulfillment of the cleansing from uncleanness. After his final covering for sin, all the various washings and sacrifices that *pointed* to him and *taught* what he would do were discarded because they were no longer needed. He was the first actual Man, the first Clean person, and through him we also are clean and don't need the blood of bulls and goats to make us spotless.
So things like the dietary laws and circumcisions are no longer commanded because those especially taught the separation of God's people from the world. After Christ's resurrection, the Gospel is for all men without regard to nationality (not that it was precisely exclusive before; the Jews were merely chosen to bear the Light of this coming truth until it was actually revealed). This is demonstrated in Peter's vision of the great sheet with all animals given to him for food: there is no longer any distinction among men except for the Name of Christ.
Mixed garments were reserved for the priests, as a special uniform. So we have this system that sets apart the Jews from the world, and more separation between the people and the priests, who essentially acted as temple/palace servants to conduct the people to God. Now all Christians have access and even a command to fulfill this role. No need for the separation. The Reformers called this the "
priesthood of all believers."
So both the Old Law and the New Law that it became both point us to Christ and teach us fundamental things about his nature. So the question becomes, does this particular Mosaic Law have more elements that are fulfilled in Christ? If it's been fulfilled, what does it teach us? And if it doesn't seem like it's been "overturned," then what is the modern application of such?
That is entirely too long an answer. But basically, it boils down to: "Adultery always will be a sin because it strikes at the faithful nature of God and what he expects of his people. Priestly/Israelitic distinctions no longer apply because Christ has brought cleansing to all through his blood."
Not all may agree with this. But I do a lot of study in Old Testament law and such and this is the gist of what my circles teach. Hope it was helpful.