A: The laws of Leviticus and Deuteronomy are part of God's covenant with the nation of Israel and have never applied to the world at large. Even rabbinic Judaism does not expect or even desire for non-Jews to keep all of these commandments. In rabbinic Judaism, a non-Jew is a "Righteous Gentile" if he keeps what are called the Seven Noachide Commandments, based on Genesis 9:1-17

1. Practice civil justice
2. Do not blaspheme
3. Do not practice idolatry
4. Do not commit incest (sometimes read to mean any sexual sin)
5. Do not commit murder
6. Do not steal
7. Do not eat flesh cut from a living animal. (sometimes read as prohibition against cruelty in general)

More importantly, the New Testament teaches in Galatians 3:23-25 and elsewhere that the Church is not under the Torah (or "Law," meaning the five books of Moses). In Acts 15 the issue arose in the early church as to whether Gentile believers should undergo conversion to Judaism. The decision of the apostles was that this was not necessary. They asked only four things of them:

1. Abstain from eating meat sacrificed to idols
2. Abstain from blood
3. Abstain from meat of strangled animals
4. Abstain from sexual immorality

(Acts 15:28-29)

This does not mean, of course, that incest, murder and thievery are acceptable forms of behavior, but these values are more or less universal, and were certainly familiar to the Greek converts. These things are mentioned elsewhere in the New Testament.(1 Corinthians 6:10, for example, or Galatians 5:19))

Notice that there is nothing in either of these lists about keeping the Sabbath or any Holy Day, or about avoiding certain kinds of meat or other food, or how to prepare a grain offering, or pay a bride price or stone a sorceress or any number of laws given to the wandering Israelites. In Galatians 4:8-11, Paul specifically chastises the Galatians for observing special days and seasons.
Paul saw the Law as a "pedagogue," using the Greek word for a slave whose job it was to usher his master's child safely to school. According to Galatians 3:24, the job of the law was to usher us to "Christ" (the Messiah). Once the "pedagogue" has delivered the child, he lets go -- otherwise his job is not done! By the same token, once we have come to Messiah, we must "let go" of the law, because otherwise it will hold us back. (Galatians 4:9) (How can a child go to school if he refuses to get off the bus?)

Of course there are good principles in the law which can still be applied ("Thou shalt not steal" for example is still a very good idea), but there a many, many rules which would only be a burden to us now. To use the bus driver analogy again, there may be some things the bus driver told you as a child that are still useful today. It's still a good idea to look both ways before crossing the street, and not to get out of a vehicle until it has come to a complete stop. But if you refuse to chew gum because a bus driver forbade it twenty years ago, that's just silly. You are no longer under that authority.
If you find an idea in Old Testament law that helps you become the kind of person that exudes love, joy, peace, patience, kindness, goodness, faithfulness, gentleness and self-control (Galatians 5:22), then that's wonderful. Do that as long as it helps. But let it go as soon as you see that Keeping the Rule has become more important to you than these things. Paul said no law can match up to these things. (Galatians 5:23)