First, this is not a matter of canon law. Canon law governs the activity of the Church as a legal entity and the powers and jurisdiction of those who have been given authority in the Church. See Code of Canon Law.
I'm not a theologian, but every Christian is called on to give answer when someone has a question (the basis of apologetics), so here is mine.
Also: I didn't take any offense at what you wrote (why should I?) and I hope you'll not take offense at the following. In my experience, there are two religious groups the Catholics admire greatly: first is the Orthodox -- they're our bosom siblings after all! even though there have been high level arguments over the last milennium; and the other is the Jews -- they're our parents after all! even though there has been a lot of misunderstanding and bad blood there as well. Ultimately, salvation is of the Jews.
My understanding, which must be overly simplified, is that the founders of Christianity held that even though the pre-gospel books of the bible (the Hebrew bible or what Christians call the old testament) are holy, the commandments therein are not binding after the coming of Jesus. This is why Christians don't follow the dietary laws, require circumcision, and so on, even though the books that give these commandments are part of the Christian bible.
The founder of the Church, of course, is God. The Church, ekklesia, is those who God calls (to holiness, to relationship with himself). Although the Church doesn't require a belief in a literal Adam and Eve, it does recognise that these first humans were the first "church", the first people God called to himself. From Adam and Eve descend all the various generations of people that we read about in the Old Covenant (and the only important ones for this question)-- the "people of the God of Abraham, Issac and Jacob"; the "Hebrews"; the "Jews"; the "Judeans". God spoke to this church through prophets and it from them that we received the written documents that come down to the last century BC, that the renewed church (which we now call the Catholic church) considers to be sacred scripture. It is in those scriptures that we find the commandments you speak of -- the "Ten Commandments" and the various religious & cultural laws that ancient Hebrews and modern Jews uphold.
Catholicism is the continuation of the People of God, the church founded by God with the creation & evolution of humanity. Jesus is God come to Earth, born of the virgin Mary, the God bearer. As such, just as he called to the first humans, so he called to the humans of the time period he was born into. As such, there was in a sense no actual "founding" of the Catholic church. It was always there: God was always there; and God's people were always there. They had always been in relationship with each other, and the people were always being called to deeper relationship.
What is binding and what is not binding. Jesus, as we all know, was a Jew. He was born into the House of David and his mother was of the priestly class. He would certainly have grown up in what we'd now call an "observant" household. What we find in his teaching is that Jesus both reveres and upholds the Law (he is God, after all!), but also turns the Law on its head and brings every law back its first principles.
Consider the story about the greatest commandment. His answer isn't the "First Commandment" or the "Fourth Commandment", but rather his answer is the "Only Commandment", which is Love. Love of God, Love of Neighbour. He steps it up by challenging conventional wisdom on who is our neighbour exactly, and so it goes on to commandment-like teachings we find in the Beatitudes and in every social teaching he makes. Everything refers back to Love. (Not "love" like "I love cheetos"; but Love like "I will sacrifice everything I have and everything I am for you".)
The result is that yes, the Commandments are binding, but also no, they're not binding in the way many people think. If you love God with all your heart, all your mind and all your strength, you're already doing what the first three commandments require. If you love your neighbour in the same way, you're already doing what fulfils the seven commandments (the Noahide Laws that apply even to Pagans and Atheists).
As far as the dietary laws and circumcision and so forth, all of those laws and indeed all of pre-Catholic scripture, points to fulfilment in Jesus. Thus, when the One who can give laws with authority sets us up only one basic law, that one law both abrogates without abrogating and summarises while at the same is the source of all just laws.
I'd like to understand what principles of theology guide the decisions about which of these laws are or are not applicable. I can't very well ask about all of Christianity (too broad!), so this question is specifically about how the Roman Catholic church decides. I'm asking about the RC church in particular because they have a long history of legal literature and canon law, so perhaps they have articulated these principles therein.
The basic principle of theology at work here is God came to Earth personally and gave us what amounts to only one Great Commandment -- let's be thankful he didn't tack on 500 more this time! Essentially, when God communicates personally and publicly, that's a pretty good hint as to which specific law is to be understood as binding or not.
For example, dietary laws. Those are matters of ritual purity, and when Jesus said that "what goes into someone's mouth doesn't make him unclean, rather, what comes out of his mouth makes him unclean", we understand by that teaching that ritual purity is not the same thing as holiness and that the practices we used to understand in terms of holiness are not what makes us holy. The long and short of it: Jesus is sanctioning us to eat a BLT sandwich, but we must always speak Truth, we must always act with Charity and we must always Love one another. We must always strive to be perfect as our Father in Heaven is perfect.
Or sex and marriage laws, which you also mentioned. When Jesus spoke against divorce, someone said that Moses allowed it. His response was that this was for the benefit of the stony hearts of man: but also that it was not always so. He then goes on not only to say "what God has put together, let no man pull apart" but speaks about adultery in the heart. Notice that with every teaching he gives, he is always stepping up the game. Just as he groomed the ancient Hebrews for holiness before, so he now grooms the Jews for even more holiness, and even closer relationship with himself.
I understand that anything that Jesus taught would have special status, but I don't think that covers everything so I suspect there's something more to it.
Indeed! We don't know everything that Jesus taught or did, and everything he taught and did is not included in the broad Tradition of the Church, whether that tradition is written (the Bible) or oral (everything else). Even the Gospel writer himself says as much when he laments Jesus did so many other things that if every one were written down, all the books in the world couldn't contain them.
What we do know is that everything in the pre-christian scripture is to be read allegorically. We do understand that some parts of the OT are historical accounts, others are liturgical prayers, other parts are wisdom literature, other parts are mythological in nature. While we might read the story of King David as an historical episode, for us that's beside the point, as he foreshadows the sacrament of Reconciliation. The idea of atoning for sin and sacrificing of self in reparation. Or the Ark of the Covenant. Indiana Jones notwithstanding, we can certainly read history into that account. There was clearly some kind of box-like object that had a definite size and was made from certain materials and held well known relics. But, again, we read the OT allegorically. Just as Eve was the mother of all humanity in the physical & social senses, and just as that Ark held the fragments of the Ten Commandments and the manna from Heaven; so we understand them to be foreshadowings of things to come. That Mary is the New Eve -- she is the mother of the Church, we are her children, not in the physical or social senses, but in the spirit. And she is also the Ark of the New Covenant: it is within her body that the Word of God resided and where the Eucharist, the Bread of Life lived his first earthly months.
So, I think, after writing that essay, the actual answer to your question is we can't answer the question because that's not how we understand the nature of scripture. The Church doesn't look at this dietary law and say "yeah, it makes a lot of sense to not eat a bloated roadkill (it's not kosher, as I understand it)" while to another law they'd say "nope! I like my BLT, so that whole pork thing is out the window!"
The whole of Jewish scripture (and naturally, when the earliest Catholics, there being no other kind of Christian at the time, say "scripture" they don't mean the Gospel, they mean Tanakh) is always interpreted by the Church as focusing in on Jesus; and the Christian scripture, the Gospels, the Letters and the Revelation are always interpreted as emanating from Jesus. He's like a lens in a telescope, but in reverse: when you look through a telescope at a star, you're seeing into the past; when you look through the Tanakh, you're actually seeing into the future.
We simply don't understand sacred legislation as it existed among the Hebrews to be applicable to Catholics (or any other Christian) in the same way. It's not that a law is binding or not binding but rather that Christ is binding: in him is all the Law and in imitating him is all fulfilment of the Law.
Does that help at all??
The Catechism is always a good primary source. In specific, the linked page describes the basic ways the scripture can be read.
There is also literally 2000 years of literature written by saints, theologians, Church Fathers, Doctors of the Church, apologists ancient and modern and just ordinary folks that puts these exegetic principles into action. You could probably pick one, say St. John Chrysostom, and spend months or years poring over hundreds of works of exegesis.
There are also many excellent modern resources both print and audio-visual. Take for example this question fielded by apologist Dr. David Anders (Called to Communion). He touches on a number of themes found in this query and in my response (simply because I learned a lot from Dr. Anders in the first place!) regarding allegorical reading of scripture, what the Bible is and how it's to be approached. I'd actually strongly recommend finding Called to Communion broadcasts on YouTube and just listen for a few hours!