I’ll address your question “Given that all of the prophesies about Jesus have not yet been fulfilled, on what Biblical basis can the Church teach that the Law was nailed to the cross?” from the perspective of your quoted text in Matthew 5. All quoted verses KJV.
Nigel is correct, your question references Colossians chapter 2 verse 14:
14 blotting out the handwriting of ordinances that was against us, which was contrary to us. He took it out of the way, nailing it to His cross;
The context of Colossians 2, most notably verses 16, 20-22, tells you unequivocally that the “handwriting of ordinances” is the Law of Moses.
16 Let no man therefore judge you in meat, or in drink, or in respect of an holyday, or of the new moon, or of the sabbath days:
20 Therefore if ye be dead with Christ from the rudiments of the world, why, as though living in the world, are ye subject to its ordinances
21 (“Touch not, taste not, handle not,”
22 which all are to perish with the using), according to the commandments and doctrines of men?
So the text is clear that Jesus took the requirements of the Law of Moses (including the commandments) and nailed them to His cross and took them out of the way for all of us who believe by faith.
However, I understand by your post that you believe there is a conflict between the apparent teachings of Jesus and the clear teaching of the NT scripture and the Apostle Paul when he clearly teaches that the law has been taken out of the way. I believe the “conflict” may be in the way you look at the words of Jesus in Matthew chapter 5.
From your post, it is clear that you believe that since Jesus said that He did not come to destroy the law and not one jot or tittle shall pass from the law until all has been fulfilled, that means that the law is still a requirement for the believer today. I believe you misunderstand Jesus’ purpose for and method of teaching the law.
Jesus taught the law better than any human scholar. The question is for what purpose did He teach it? Jesus taught the law to convict everyone of sin especially those who denied their own sin. His audience always included the religious leaders (Pharisees, Sadducees, scribes, etc) of His day. Those religious leaders all believed that as long as they kept the Law of Moses they would avoid sin and thereby be acceptable to God. Jesus sought to convict these religious self righteous people by teaching the gravity of keeping the Law of Moses. Jesus elevated the keeping of the law to become unattainable for any human being. Jesus taught the law to convict everyone who heard it of their sin for no one can keep the Law of Moses.
If you look at the Sermon on the Mount again, you will see a pattern, You will see Jesus starts out with what everyone understood about the law (do not murder, do not commit adultery, etc) but then he raises the bar to become unattainable for any human. He states it’s not just the murder, it’s about hating or being angry with your brother; it’s just not the actual adultery but it's also lusting. He brings the actual commandment from being just an external action to an internal motivation and emotion. No one can pass this test.
Jesus’ intention was to teach the law in such a way as to make it impossible for anyone to think they are without sin. That’s why He stated in Matthew 5:20, “that except your righteousness shall exceed the righteousness of the scribes and Pharisees, ye shall in no case enter into the kingdom of heaven”. Anyone who heard that understood that He meant that no one can enter Heaven on their own. This is why Jesus also taught, “come to me all ye that labor and are heavy laden and I will give you rest.”
A perfect example of Jesus using the Sermon on the Mount to convince the Pharisees that the Law of Moses could not save them was the example of divorce in Matthew 5: 31 and 32. In these verses, Jesus appears to contradict the Law of Moses which clearly allows divorce. Here in Matthew 5, Jesus states that divorce is sinful. This teaching then spurred the Pharisees to confront Jesus about His teaching.
The Pharisees came to Jesus on two separate occasions (Matthew 19 and Mark 10) asking Him if it was lawful for a man to divorce his wife for any reason. On both occasions, Jesus did not answer their question. Instead, He gave them evidence on how divorce was sinful. He stated that divorce was allowable by Moses (at God’s direction) because of the hardness of the hearts of men. (God allowed divorce so the woman could be cared for). However, Jesus also instructed them, that “from the beginning” this was not the case; God’s “original intention” was for one man – one woman for the duration of their lives. Any other situation would have been sinful.
So, we see that the reason that Jesus did not answer the Pharisees' question about the legality of divorce was that it was not a worthy question to answer. Of course, divorce was lawful as provided by the Law of Moses but that was not the point. The Pharisees were seeking to justify their divorces because they believed that as long as they acted in accordance with the law, that their behavior was not sinful. Jesus sought to convince them that their behavior, although in line with the Law of Moses, was still sinful. This is a perfect example of Jesus using the Law to convict the Pharisees of their sin which they always denied.
I’ll conclude with one other point regarding Matthew 5:18:
18 For verily I say unto you, Till heaven and earth pass, one jot or one tittle shall in no wise pass from the law, till all be fulfilled.
Please remember that Jesus fulfilled every aspect of the Law of Moses so that’s why Paul could say in Romans 10:4:
For Christ is the end of the law for righteousness to every one that believeth.