Luke 16:16 The law and the prophets were until John: since that time the kingdom of God is preached, and every man presseth into it.
The old covenant with and through Israel of the law and the prophets, ended with John the Baptist. He was the last prophet under the law, making the way for a new covenant. The new covenant was accomplished through Jesus, his blood shed for our sins, his resurrection from the grave and grace received through faith in him. I see the new covenant as for every man, whosoever who will come to Jesus. The crowds pressed to get to Jesus, so we must be determined to receive from him eternal life. There is opposition from the flesh and the devil, but the truth shall make you free, press in and receive life more abundant and everlasting.
Luke 16:17 And it is easier for heaven and earth to pass, than one tittle of the law to fail.
A tittle, a point, the minute point or stroke added to some letters of the Hebrew alphabet to distinguish them from others which they resemble; hence, the very least point. (Easton's Bible Dictionary) Jesus is saying that God's law is true and will remain true. Jesus fulfilled all the law, so by receiving Jesus we are in agreement with the law and being in him, we are free from the curse of failing the law. We are safe in Jesus, God's wrath will not come to us for failings. It is the grace of God we receive through faith in him. Praise God!
Luke 16:18 Whosoever putteth away his wife, and marrieth another, committeth adultery: and whosoever marrieth her that is put away from her husband committeth adultery.
Now why did he bring this up? Why? Because it is God's pure law. So many people ignore this law and divorce and remarry for something better. No, it is adultery. If you are not in Christ Jesus, you will be judged by this law. If you are in Jesus, you certainly willfully will not do this? Jesus is our refuge, but let us not continue to sin willfully.
Rom 6:1 What shall we say then? Shall we continue in sin, that grace may abound?
Rom 6:2 God forbid. How shall we, that are dead to sin, live any longer therein?
Rom 6:3 Know ye not, that so many of us as were baptized into Jesus Christ were baptized into his death?
Rom 6:4 Therefore we are buried with him by baptism into death: that like as Christ was raised up from the dead by the glory of the Father, even so we also should walk in newness of life.
Rom 6:5 For if we have been planted together in the likeness of his death, we shall be also in the likeness of his resurrection:
Rom 6:6 Knowing this, that our old man is crucified with him, that the body of sin might be destroyed, that henceforth we should not serve sin.
Rom 6:7 For he that is dead is freed from sin.
Rom 6:8 Now if we be dead with Christ, we believe that we shall also live with him:
Rom 6:9 Knowing that Christ being raised from the dead dieth no more; death hath no more dominion over him.
Rom 6:10 For in that he died, he died unto sin once: but in that he liveth, he liveth unto God.
Rom 6:11 Likewise reckon ye also yourselves to be dead indeed unto sin, but alive unto God through Jesus Christ our Lord.
Rom 6:12 Let not sin therefore reign in your mortal body, that ye should obey it in the lusts thereof.
Rom 6:13 Neither yield ye your members as instruments of unrighteousness unto sin: but yield yourselves unto God, as those that are alive from the dead, and your members as instruments of righteousness unto God.