To begin, it should be understood that the word "ordinances" in Colossians 2:14 and Ephesians 2:15 does not refer to God's laws. It is translated from the Greek word dogma and refers generally to opinions, judgments, and decrees. Such ordinances could be public decrees by government officials or religious decrees by religious officials. We should, however, treat these two verses separately because they deal with different subjects.
Colossians 2:14 should be seen in its context, specifically with the preceding verse:
And you, being dead in your trespasses and the uncircumcision of your flesh, He has made alive together with Him, having forgiven you all trespasses, having wiped out the handwriting of requirements that was against us, which was contrary to us. And He has taken it out of the way, having nailed it to the cross. (verses 13-14)
The New King James version has rendered dogma as "requirements," a perfectly justifiable translation. The phrase "handwriting of requirements," however, begs an explanation. Its basic meaning is "a written statement of obligation," much like a traffic citation, which lists the laws that its recipient broke. Thus, it is a record of wrongdoing or guilt. We can verify this by seeing that the clause in which it appears restates the one just before it: "having forgiven you all trespasses." What Paul is telling these Colossians is that the sacrifice of Jesus Christ has "wiped out" all record of their guilt in breaking God's law. That is good news!
Christ came to pay the penalty for all our sins. Accepting His sacrifice releases us from the penalty of death incurred through our sin and cleanses our conscience from all guilt (Ephesians 1:7; Hebrews 9:14; I John 1:7; 2:2). God says that when He forgives our sins, He removes it "as far as east is from the west" (Psalm 103:12). This truly is "tak[ing] it out of the way"!
Ephesians 2:15 uses dogma in a different way, and again, we need to see the context of Paul's argument:
For He Himself is our peace, who has made both [Jew and Gentile] one, and has broken down the middle wall of division between us, having abolished in His flesh the enmity, that is, the law of commandments contained in ordinances, so as to create in Himself one new man from the two, thus making peace, and that He might reconcile them both to God in one body through the cross, thereby putting to death the enmity. (Verses 14-16)
Paul himself defines what this "law of commandments contained in ordinances" is; it is "the enmity"—which he mentions twice (verses 15-16)—between Jews and Gentiles (see verses 11-12). He also calls it "the middle wall of division" in verse 14. Whatever "the law of commandments contained in ordinances" is, it causes hatred and division. This rules out right away that it refers to God's law, for it, Paul writes in Romans 7:12, "is holy, and the commandment holy and just and good."
We can solve our dilemma with one passage from Jesus' own mouth, speaking to the scribes and Pharisees of His day:
Why do you also transgress the commandment of God because of your tradition? . . . Thus you have made the commandment of God of no effect by your tradition. Hypocrites! Well did Isaiah prophesy about you, saying: . . . "And in vain they worship Me, teaching as doctrines the commandments of men." (Matthew 15:3-9)
These "commandments of men" were the restrictive pharisaical decrees burdening the Jews and those among the Gentiles who desired to worship God. These human ordinances—additions by men to what God revealed in the Old Testament—contributed to feelings of prejudice, animosity, suspicion, and separation between the Jews and Gentiles who were being called into God's church. These ordinances acted as a "middle wall of division." However, Jesus abolished that barrier through His supreme sacrifice: "For He Himself is our peace" (Ephesians 2:14).
In Paul's day, many newly-begotten Christians continued to suffer from the burden of their former teachings. Some converted Jews found it difficult to forget and change that deeply-ingrained part of their lives. It affected even someone as converted as the apostle Peter (see Galatians 2:11-12). Paul explains to the Ephesians, mostly Gentiles, that Christians comprise an entirely new community that is not dependent at all upon the manmade laws and regulations of their former religions, but only upon what God had revealed: "Now, therefore, you are no longer strangers and foreigners, but fellow citizens with the saints and members of the household of God, having been built on the foundation of the apostles and the prophets, Jesus Christ Himself being the chief cornerstone" (Ephesians 2:19-20).
Christ abolished the Talmudic traditions—all of which were yokes of bondage (Galatians 5:1; Matthew 23:4)—as necessary for salvation. Jesus, however, did not do away with any part of God's law. In fact, He made it possible for both Jew and Gentile to become spiritual Israelites, the children of God (Galatians 3:26-29; 6:16), so they might live together in freedom within His perfect law (James 1:25). He says in Matthew 5:17, "Do not think that I came to destroy the Law or the Prophets. I did not come to destroy but to fulfill."
Yes, to fulfill, to observe, to keep, and by doing so, He set us a perfect example as to how we ought to live. We are "to walk just as He walked" (I John 2:6). The apostle Peter writes that Christ left "us an example, that you should follow His steps" (I Peter 2:21). Paul says, "Imitate me, just as I also imitate Christ" (I Corinthians 11:1).
God's law is good and for our benefit: "You shall therefore keep His statutes and His commandments, which I command you today, that it may go well with you and with your children after you, and that you may prolong your days in the land which the LORD your God is giving you for all time" (Deuteronomy 4:40).
Jesus Christ did indeed do away with the unnecessary and unprofitable requirements of men, but the law of God is binding on us more than ever. We are to keep it in the Spirit as well as the letter. Even so, the benefits of keeping God's laws are wonderful and many. Jesus says, "If you know these things, happy are you if you do them" (John 13:17).