Thanks for your inquiry. As you mentioned in your question, the Old Testament law contains a number of specific commandments: regulations regarding widths and heights and materials and clothing, to name a few. How do all these details -- and the rest of the law -- relate to you and to me today?
First, it is helpful to note that the Old Testament contains three types of law: ceremonial, civil and moral. The ceremonial laws addressed such issues as the temple regulations and the various sacrifices. The civil laws dealt with circumstances within the state of Israel, such as how to treat adulterers. The moral law, which is contained summarily in the Ten Commandments, is "written on the heart" (Romans 2:15) of all people and is binding on all humans in all places at all times.
In answering your question, we should recall at the outset that the Lord Jesus Christ came not to destroy but to fulfill all of the law -- yet he also gave new laws to his followers through his inspired apostles (e.g. Ephesians 4:17, Philippians 2:12b). So what does the coming of Christ mean for you and for me in regard to the law of God?
First, Jesus fulfilled the ceremonial laws, in that he was God with us (the true Temple of God); through his perfect obedience to those laws; and especially through his one, perfect, final and complete sacrifice for sin at Calvary. The OT ceremonial laws ended with the work of Christ at the cross. You and I can approach the infinite God through the intercession of our great High Priest.
Second, Jesus fulfilled the civil laws by obeying them perfectly and by demonstrating that a true Israelite was any person, regardless of birth, who looked by faith to him for salvation (Romans 9:6). As the New Testament plainly teaches, God no longer rules His people through an organized nation-state called "Israel" (or anything else for that matter); thus a Christian does not have to abide by the state-laws of Old Testament Israel.
Third, Jesus fulfilled the moral laws of the Old Testament both in his life and in his doctrine. Not only was he "made under the law" to redeem you and me who have failed to keep the moral law of God perfectly (Galatians 4:1-5, St. Matthew 5:48) through his sacrifice for sins; he obeyed the law so that you and I might be credited with his righteousness (another term for "perfect obedience to the law").
Thus through faith in Christ, who fulfilled the Old Testament laws in his person and in his work, you are 1) forgiven for breaking the moral law of God and 2) credited with Jesus' perfect obedience to the moral law. What a "grand transaction," as an astute theologian once observed!
If you believe on Christ as your Redeemer, then, are you free from the Old Testament laws? Yes and no.
Yes, you are free from having to keep the civil and ceremonial laws. They were temporary and have been fulfilled by Christ. Yes, you are free from the fear of God's wrath from not having kept His law perfectly.
But no, you are not free to "live like you want." If you'll notice, Jesus not only reiterates some of the Ten Commandments in his Sermon on the Mount -- he actually adds to them! For example, adultery becomes more than a physical act; it now involves thoughts. Time and again the New Testament writers call Christians to live out the implications of their faith, and that same New Testament ethic is derived from the Ten Commandments/moral law of the Old Testament.
The Old Testament laws, therefore, show you and me our need for the Savior as well as his perfect fulfillment of them. The moral law also serves as a guide for you in your Christian life.
To put it another way: you can eat shellfish if you want; the ceremonial law is past. You can live in a country that doesn't call for the stoning of adulterers; the civil law has been abrogated. But it never has been acceptable for you to steal, to worship idols, to covet or to break any of the other moral laws of the Old Testament, laws that are written on every person's heart. Those laws transcend time and culture.
So what about all those heights and weights and measurements? How do they relate to you today? Basically, those laws point to God's desire to have a people to Himself who thoroughly followed His commandments and therefore went against the flow of the pagan world around them. He wanted them to obey Him. He wanted Israel to be different. And he was and is a God of detail.
How amazing that Christ has fulfilled all of the law of God for you and me -- and not ignored one jot or tittle (II Peter 1:1). May our lives be lives of obedience and praise to our perfect and glorious Savior!