Did he ever explicitly say which ones you're exempt from though? I don't know of there being an exhaustive list of specifics but maybe there is.
For the churches that actually care about that sort of thing, there's normally a distinction made between moral, civil, and ceremonial Mosaic law.
The moral law is stuff like the Ten Commandments. Broad, nonspecific, "don't do this stuff, it's bad". These laws are a general expression of how God wants us to act.
Civil law is the ridiculously specific stuff that you get in Leviticus, that sets rules for slave ownership and property rights and all that. These were relevant to ye olde nation of Israel, basically God's divinely ordained legal system. You can argue that we should use these as a basis for modern law, but there's not really any point. I mean, who has slaves any more, geez.
Similarly, ceremonial laws are for the priesthood, sacrifices, and other religious... ceremonies. These were specifically relevant to Judaism, and were absolutely made redundant by Christ. When these laws are cited in a modern context it's usually to defend the idea that we should be building big, fancy churches, and generally putting a lot of money and effort into worship. Which has some merit IMO, but if it gets in the way of, say, providing for the poor, then you're flagrantly missing the point.
So basically, moral law is always relevant. Do not murder, do not lie, provide for those in need, hold God in the highest esteem.
Civil law is arguably relevant (but not really). Sell your land after seven years, don't keep your slaves forever (unless they want to stay), killing someone by accident is forgiveable if you go to this city afterwards.
Ceremonial law is redundant and only vaguely relevant for modern worship. Sacrifice X animal on Y day, sprinkle blood here, there, and everywhere, an aroma pleasing to the Lord, etcetera.