Noachide Covenant is eternal:
Genesis 9:8-16 : Then God said to Noah and to his sons with him, "As for me, I am establishing my covenant with you and your descendants after you, and with every living creature that is with you, the birds, the domestic animals, and every animal of the earth with you, as many as came out of the ark. I establish my covenant with you, that never again shall all flesh be cut off by the waters of a flood, and never again shall there be a flood to destroy the earth." God said, "This is the sign of the covenant that I make between me and you and every living creature that is with you, for all future generations: I have set my bow in the clouds, and it shall be a sign of the covenant between me and the earth. When I bring clouds over the earth and the bow is seen in the clouds, I will remember my covenant that is between me and you and every living creature of all flesh; and the waters shall never again become a flood to destroy all flesh. When the bow is in the clouds, I will see it and remember the everlasting covenant between God and every living creature of all flesh that is on the earth."
Covenant with Abraham and his offspring is eternal:
Genesis 15:18: In the same day the LORD made a covenant with Abram, saying, Unto thy seed have I given this land, from the river of Egypt unto the great river, the river Euphrates.
Genesis 17:7-9 : I will establish my covenant between me and you, and your offspring after you throughout their generations, for an everlasting covenant, to be God to you and to your offspring after you. And I will give to you, and to your offspring after you, the land where you are now an alien, all the land of Canaan, for a perpetual holding; and I will be their God." God said to Abraham, "As for you, you shall keep my covenant, you and your offspring after you throughout their generations.
Sinai Covenant with Israel (and its resident aliens) is eternal:
Numbers 15:15 : As for the assembly, there shall be for both you and the resident alien a single statute, a perpetual statute throughout your generations; you and the [resident] alien shall be alike before the LORD.
Deuteronomy 4;35-40 : To you it was shown so that you would acknowledge that the LORD is God; there is no other besides him. From heaven he made you hear his voice to discipline you. On earth he showed you his great fire, while you heard his words coming out of the fire. And because he loved your ancestors, he chose their descendants after them. He brought you out of Egypt with his own presence, by his great power, driving out before you nations greater and mightier than yourselves, to bring you in, giving you their land for a possession, as it is still today. So acknowledge today and take to heart that the LORD is God in heaven above and on the earth beneath; there is no other. Keep his statutes and his commandments, which I am commanding you today for your own well-being and that of your descendants after you, so that you may long remain in the land that the LORD your God is giving you for all time.
Deuteronomy 29:29 : The secret things belong to the LORD our God, but the revealed things belong to us and to our children forever, to observe all the words of this Law.
1 Chronicles 16:13-18 : O offspring of his servant Israel, children of Jacob, his chosen ones. He is the LORD our God; his judgments are in all the earth. Remember his covenant forever, the word that he commanded, for a thousand generations, the covenant that he made with Abraham, his sworn promise to Isaac, which he confirmed to Jacob as a statute, to Israel as an everlasting covenant, saying, "To you I will give the land of Canaan as your portion for an inheritance."
Isaiah 55:3 Incline your ear, and come to me; listen, so that you may live. I will make with you an everlasting covenant, my steadfast, sure love for David.
Isaiah 24:5 The earth also is defiled under the inhabitants thereof; because they have transgressed the laws, changed the ordinance, broken the everlasting covenant.
Psalm 103:17-18: But the mercy of the LORD is from everlasting to everlasting upon them that fear him, and his righteousness unto children's children; To such as keep his covenant, and to those that remember his commandments to do them.
Psalm 105:6-11: O offspring of his servant Abraham, children of Jacob, his chosen ones. He is the LORD our God; his judgments are in all the earth. He is mindful of his covenant forever, of the word that he commanded, for a thousand generations, the covenant that he made with Abraham, his sworn promise to Isaac, which he confirmed to Jacob as a statute, to Israel as an everlasting covenant, saying, "To you I will give the land of Canaan as your portion for an inheritance."
Exodus 31:16-17: Wherefore the children of Israel shall keep the Sabbath, to observe the Sabbath throughout their generations, for a perpetual covenant. It is a sign between me and the children of Israel for ever.
It has been said (by Saint Paul in Christianity) that upon Messiah's arrival the prophecy of Jeremiah 31:31 will render the Torah Commandments (i.e. what Saint Paul calls "the Law" in Greek) obsolete. Nothing could be farther from the truth. The prophecy of Jeremiah 31:31 does say that there will be a new Covenant, but it is very clear that the difference between the new and the old is only that in the new Covenant the same Laws will apply except that they will no longer have to be learned or taught because people will have them implanted in their hearts.
Confirming that the Laws are still valid even into the Messianic Age, witness the following verses from the Torah, in which it is clear that even the ritual laws are still valid after the Kingdom of God is instated:
Isaiah 56:1, 56:3, 56:6-8: "Thus says the Lord: Maintain justice, and do what is right, for soon my salvation will come, and my deliverance revealed. ... Do not let the foreigner joined to the Lord say "The Lord will surely separate me from his people" ... And the foreigners who join themselves to the Lord, to minister to him, to love the name of the Lord, and to be his servants, all who keep the sabbath, and do not profane it, and hold fast my covenant - these I will bring to my holy mountain, and make them joyful in my house of prayer; their burnt offerings and their sacrifices will be accepted on my altar for my house shall be called a house of prayer for all peoples. Thus says the Lord God who gathers the outcasts of Israel: "I will gather others to them besides those already gathered.""
Zechariah 14:16 Then all who survive of the nations that have come against Jerusalem shall go up year after year to worship the King, the Lord of Hosts, and to keep the festival of Booths.