Old Testament Law

What do we do with all those OT Laws?  When some smug atheist asks you if, as a Christian you wear woolen blends (Deut 22:11 ), how do you answer? 
What about eating pork, not working on the Sabbath, etc?  What do we do with these Old Testament Laws that they like to quote out of Leviticus and Deuteronomy?  Do we really just pick and choose what we like, as we're accused of? 
Well, here are some answers to these ridiculous accusations, in order to answer the fool, lest they be wise in their own eyes (Proverbs 26:5)

The Law can be divided into three categories:  Moral, Civil, and Ceremonial. 

The Ceremonial Laws (animal sacrifices, the Sabbath, etc) were pointing us to a coming Messiah, and so this aspect of the Mosaic Law has been set aside, fulfilled in Christ.

Colossians 2:14-17
having canceled the written code, with its regulations, that was against us and that stood opposed to us; He took it away, nailing it to the cross.  And having disarmed the powers and authorities, He made a public spectacle of them, triumphing over them by the cross.
Therefore do not let anyone judge you by what you eat or drink, or with regard to a religious festival, a new moon celebration or a Sabbath day.  These are a shadow of the things that were to come; the reality, however, is found in Christ.

The Civil Laws were written to a specific people at a specific time and specific place. The basic responsibility for the civil aspect, showing the application of the moral Law in a community, has been transferred to human government. 

Romans 13:1
Everyone must submit himself to the governing authorities, for there is no authority except that which God has established.  The authorities that exist have been established by God.

The Moral Law finds its basis in the character of God and is presented in outline form in the Ten Commandments. It still stands and applies to our lives now, having never been revoked or abolished, but finds its authority in the New Covenant. 
Every unbeliever is still under its requirement of perfection and its condemnation, until he comes to Christ, and every believer still finds in it the standard for behavior. 

Romans 8:3-4
For what the Law could not do, weak as it was through the flesh, God did:  sending His own Son in the likeness of sinful flesh and as an offering for sin, He condemned sin in the flesh, so that the requirement of the Law might be fulfilled in us, who do not walk according to the flesh but according to the Spirit.

Normally, unbelievers like to quote the most obscure Ceremonial or old Civil Laws, but the real problem they have concernes the Moral Law and submission to the Lord.