This is a very ... complicated matter. Hopefully I speak somewhat clearly. Errr... type.
Not one will pass away "until all is accomplished." And to be honest, I'm not sure what exactly Jesus is referring to there, but it "accomplish" sounds rather similar to "fulfill." Perhaps Jesus is talking about what He came to accomplish? But at this point, He is still giving the Jews a chance to *not* reject Him. He's talking as if He is not going to die, as if He actually will be accepted as the Jewish Messiah by the Jews.
Also, it is important to see who He is talking to. In Luke, He's talking to the pharisees. Justifying their own faults (REAL faults, according to the actual law) while simultaneously trying to make sure everyone else kept not just the Law, but the traditions.
This is why the rest of the NT is important, understanding why Jesus came (super short version, He came to Israel as their Messiah under/in the Old Covenant; but He was rejected, and a New Covenant was made that was not specific to Israel... hence the rest of the NT). Under the old covenant with Israel, what Jesus said totally makes sense. You can't say you don't have to follow parts of the Law. Furthermore, you can't wiggle around it like the pharisees (hey, I didn't sin! I mean I was angry enough to WANT to kill my brother, but I didn't, so I'm innocent of the law!).
But, yes, that changed. Jesus was rejected. Jesus still fulfilled the law. Paul, in Romans, goes through great lengths to discuss this, going back to what the law was even there for to begin with. The author of Hebrews does, as well. Paul even mentions that the Jews rejected Jesus so that salvation would be extended to the gentiles. In other words, since the Jews rejected Jesus as Messiah, a new covenant was made that was NOT with Israel specifically, and thus all can come, and without going through the Old Covenant (hence the lack of circumcision being necessary, as Paul makes pretty clear in ... now I forget which epistle).
For a Jew living in the Old Covenant, to say that one of God's covenant laws was not necessary? Blasphemy, pretty much.
"Unchanging" does not refer to God's methods or actions, it refers to His character. Unchanging, faithful, true, those would all be very related words. It doesn't mean that how God acts or deals with men doesn't change. Clearly, that has changed, since Israel was not around since the beginning of time.