The authority and relevance of the Old Testament books can be questioned and the Old Testament covenant and teachings regarded as null and void because of the cross. But Jesus' finished work does not completely erase the old covenant, rather it has fulfilled it and that's why it's so important to understand it.
Hebrews 8:13 tells us, "In speaking of a new covenant, he makes the first one obsolete. And what is becoming obsolete and growing old is ready to vanish away." This scripture has long been used as proof that all of the Mosaic Law and teaching of the prophets are now worthless to us because of the new covenant.
People look to laws on tithing, for instance, and say that because we are now under grace, God does not require that we give ten percent of our earnings to the work of the Lord. While it's true that tithing is no longer obliged of us, the tenet of the tithe still lives - that being, that we acknowledge God's ownership of our wealth and His desire for us to trust Him enough to return a portion of our earnings to Him.
There is, however, truth to the idea that some parts of the Mosaic Law are no longer applicable - at least in the same way - because of God's redemptive work on the cross. Some of those laws include laws on sacrifices that we are no longer required to perform because Jesus paid the price once and for all. And there are others laws that really are no longer relevant, such as dietary prohibitions.
But no matter how much of the Old Covenant laws no longer apply, much of the principle still remains. God still values holiness and despises sin. The New Covenant is not to be used as a license to sin because God's attitude towards sin has not changed. That's not to say that we are to act perfect because we are not, but our heart towards sin should be completely changed once we submit ourselves to the fullness of Christ.
But God abolishing the law does not necessarily mean that He scraps the whole thing and throws it in the junk. Jesus says it best in Matthew 5:17, "Do not think that I have come to abolish the Law or the Prophets; I have not come to abolish them but to fulfill them."
To say that we scrap the whole Mosaic Law would be overkill. God still desires that we avoid lying and coveting, but now because of what Christ has done for us on the cross, there is a new righteousness and grace. Moreover, Jesus' finished work gives us access to the Holy Spirit that teaches our hearts to say no to sin and when we truly understand what He has done for us, we will, as Paul discovered, want to only be slaves to Him and not to our sinful desires.
