Are the laws of the Old Testament still binding?

No, Christians are not under the OT law.Luke 16:16

The law and the prophets were until John [the Baptist]: since that time the kingdom of heaven is preached.Romans 6:14

Ye are not under the law, but under grace.Romans 7:4, 6

Ye also are become dead to the law by the body of Christ .... We are delivered from the law, that being dead.Romans 10:4

Christ is the end of the law for righteousness to every one that believeth. 2 Corinthians 3:14

But their minds were blinded: for until this day remaineth the same veil untaken away in the reading of the old testament; which veil is done away in Christ.Galatians 3:13

Christ hath redeemed us from the curse of the law.Galatians 3:24-25

Wherefore the law was our schoolmaster to bring us unto Christ, that we might be justified by faith. But after that faith is come, we are no longer under a schoolmaster.Galatians 5:18

But if ye be led of the Spirit, ye are not under the law.  Ephesians 2:15

Having abolished in his flesh the enmity, even the law of commandments contained in ordinances.Colossians 2:14

Blotting out the handwriting of ordinances ... nailing it to his cross.

Then you will know the truth, and the truth will set you free.”

 ³³ They answered him, “We are Abraham’s descendants and have never been slaves of anyone. How can you say that we shall be set free?”

 ³⁴ Jesus replied, “Very truly I tell you, everyone who sins is a slave to sin. ³⁵ Now a slave has no permanent place in the family, but a son belongs to it forever. ³⁶ So if the Son sets you free, you will be free indeed. John 8:32-36