“For as man, disobeying, drew death upon himself; so, obeying the will of God, he who desires is able to procure for himself life everlasting. For God has given us a law and holy commandments; and every one who keeps these can be saved, and, obtaining the resurrection, can inherit incorruption.” – St. Theophilus of Antioch, to Autolycus (Book 2, Chapter 27) [link]
Are we still under a Law? Yes. However, we are not under the Mosaic one.
The Mosaic Law worked for a while, but ceased to be the best option after the “time of reformation” (Hebrews 9:10). At this time, Christ came to redeem humanity (Hebrews 9:15) and to universalize the Law and open it up to the Gentiles (Acts 28:28, Romans 11:11), which He could have done within Judaism if the Jewish leaders had not rejected Him (He is “the stone which the builders rejected” – Mark 12:10). Due to His work, we are now under “a better covenant” (Hebrews 8:6).
None of this means that we are now apart from a Law.
Christ commanded us to “treat people the same way [we] want them to treat [us], for this is the Law and the Prophets” (Matthew 7:12). He said to do something, and then gave as His reason that it is the intent of the Law. He also positively referenced the Law in Luke 10:25-28. A lawyer asked what is required to “inherit eternal life,” and Christ asked the man to look to the Law. The lawyer said that the Law commands us to “love [Him] with all [our] heart, and with all [our] soul, and with all [our] strength, and with all [our] mind; and [our] neighbor as [ourself].” Christ replied, “You have answered correctly; do this and you will live.”
In Mark 10, a wealthy man asks Christ what is required to reach Heaven, and Christ cites the Ten Commandments (v. 17-19). The man says that he already observes them, but Christ corrects him and cleverly makes the point that the man must practice charity, which the man, unfortunately, refuses (v. 20-22). Christ was not adding anything new to the Law, but was getting at the intent of it — charity was already commanded in the Old Testament (Proverbs 19:17, Proverbs 21:13, Sirach 29:8-13)!
Paul realized that, because a man “hung on a tree” (here, “tree” would equal a wooden cross) is cursed according to the Mosaic Law (Deuteronomy 21:22-23) and Christ most certainly did not deserve to be cursed, at least some parts of it are no longer binding. Christ both took upon Himself the penalties for sins committed under the Mosaic Law and opened “the blessing of Abraham” and “the promise of the Spirit” up to the Gentiles (Galatians 3:13-14).
Paul did not, however, reject the necessity of good works. When Paul denounces “works of the Law,” he is referring to things such as ritual circumcision. Passages like Romans 3:27-30 and Galatians 3:27-29, which are surrounded by statements that seem to advocate “faith alone,” are key to understanding Paul’s thoughts. Paul placed emphasis on the facts that Jews and Gentiles 1) serve the same God, 2) share a common heritage, and 3) are judged by the same general standards — we are all “one in Christ Jesus”. That is partially why he so strongly insisted on the universality of Christ, the importance of faith, and the worthlessness of divisive cultural practices (e.g. circumcision).
Does the existence of a Law always “nullify the grace of God” or mean that “Christ died needlessly” (Galatians 2:21)? Absolutely not. First, it makes His grace remarkably plain. If He did not provide us with a path to redemption and salvation, then His justice would demand our damnation. To provide us with a Law is merciful of Him. Second, it is still only through Christ that anyone can attain salvation. “[N]o one comes to the Father but through [Him]” (John 14:6).
Truly, “what matters is the keeping of the commandments of God” (1 Corinthians 7:19) and “unless [our] righteousness surpasses that of the scribes and Pharisees, [we] will not enter the kingdom of heaven” (Matthew 5:20).
This all undermines the idea that we are not bound by a Law. The Law will not fail (Matthew 5:18, Luke 16:17). We are still under a Law, minus Mosaic cultural practices. “[H]e who does the will of [God]” will reach Heaven (Matthew 7:21), and God will say, “Depart from me,” to those who “practice lawlessness” (Matthew 7:23).
“Do we then nullify the Law through faith? May it never be! On the contrary, we establish the Law.” – Romans 3:31
(All verses are from the NASB translation, except for the passage from Sirach, which is from the RSV translation.)
Martin Luther said and wrote many heretical things, but here are a mere five quotes, along with Biblical passages that disprove them.
1. “For reason is directly opposed to faith. This is why you must let reason go. It must be killed and buried in believers.” 
(Answer: Proverbs 14:15, Colossians 1:9, Colossians 4:5-6, 1 Thessalonians 5:19-22)
2. “..[A Christian] could not lose his salvation, however much he sinned, unless he refused to believe. For no sin can condemn him save unbelief alone.” 
(Answer: Hebrews 10:26-27)
3. “Be a sinner, and let your sins be strong, but let your trust in Christ be stronger, and rejoice in Christ who is the victor over sin, death, and the world. We will commit sins while we are here, for this life is not a place where justice resides. …No sin can separate us from Him, even if we were to kill or commit adultery thousands of times each day.” 
(Answer: Psalm 4:4, Matthew 5:48, Hebrews 10:26-27)
4. “It is good that we have such a man [Jesus Christ], because God in himself is cruel and bad.” 
(Answer: Psalm 51:1, Jeremiah 9:24, Jeremiah 31:3)
5. “I miss more than one thing in this book [Revelation, aka Apocalypse], and this makes me hold it to be neither apostolic nor prophetic…and [I] can nohow detect that the Holy Spirit produced it. …My spirit cannot fit itself into this book.” 
(Answer: Revelation 22:19)
1. Luther’s Sermon on Matthew 19:13-15. “What Luther Says,” 1:485-486 (entry 1440). [link]
3. Let Your Sins Be Strong: A Letter From Luther to Melanchthon. Translated by Erika Bullmann Flores. [link]
5. M. Reu, Luther’s German Bible: An Historical Presentation Together with a collection of Sources (Ohio: The Lutheran Book Concern, 1934) 174-175 [link]