What in New Testament invalidates God’s commandments from the Old Testament? Where in the New Testament  (if at all) does it say that Christians do not have to abide God’s commandments from the Old Testament?
The Old Testament contains many commandments.
Some of them the New Testament explicitly says are still in force. In Jesus' Sermon on the Mount he addresses some of these, including murder, adultery, and covetousness.
Some of them the New Testament explicitly says are obsolete. That includes all regulations surrounding temple worship. As Jesus told the woman at the well in John 4:

21 “Woman,” Jesus replied, “believe me, a time is coming when you will
worship the Father neither on this mountain nor in Jerusalem. 22 You
Samaritans worship what you do not know; we worship what we do know,
for salvation is from the Jews. 23 Yet a time is coming and has now
come when the true worshipers will worship the Father in the Spirit
and in truth, for they are the kind of worshipers the Father seeks. 24
God is spirit, and his worshipers must worship in the Spirit and in
truth.”

The entire Book of Hebrews speaks of the old sacrificial system and how it really pointed to Jesus and his death on the cross. Since Jesus has paid the price once and for all time, no more blood sacrifices are necessary.
Another regulation concerns circumcision. The early church argued fiercely about this, but the Apostle Paul confronted the church leadership over the issue and they agreed that Gentile believers did not need to be circumcised. You can read about this in Acts 15:

6 The apostles and elders met to consider this question. 7 After much
discussion, Peter got up and addressed them: “Brothers, you know that
some time ago God made a choice among you that the Gentiles might hear
from my lips the message of the gospel and believe. 8 God, who knows
the heart, showed that he accepted them by giving the Holy Spirit to
them, just as he did to us. 9 He did not discriminate between us and
them, for he purified their hearts by faith. 10 Now then, why do you
try to test God by putting on the necks of Gentiles a yoke that
neither we nor our ancestors have been able to bear? 11 No! We believe
it is through the grace of our Lord Jesus that we are saved, just as
they are.”
...
19 “It is my judgment, therefore, that we should not make it difficult
for the Gentiles who are turning to God. 20 Instead we should write to
them, telling them to abstain from food polluted by idols, from sexual
immorality, from the meat of strangled animals and from blood. 21 For
the law of Moses has been preached in every city from the earliest
times and is read in the synagogues on every Sabbath.”

The latter part of the quote gives the highlights of what parts of the Law were to remain in force: no idol worship or participation in pagan rituals, humane slaughter of animals, and no sexual immorality.
The Apostle Paul also spoke to the issue of celebrating the Jewish holidays, saying that they were not obligatory. In Galatians 4 he says:

8 Formerly, when you did not know God, you were slaves to those who by
nature are not gods. 9 But now that you know God—or rather are known
by God—how is it that you are turning back to those weak and miserable
forces[d]? Do you wish to be enslaved by them all over again? 10 You
are observing special days and months and seasons and years! 11 I fear
for you, that somehow I have wasted my efforts on you.

And in Romans 14, Paul says:

5 One person considers one day more sacred than another; another
considers every day alike. Each of them should be fully convinced in
their own mind. 6 Whoever regards one day as special does so to the
Lord.

This still leaves many parts of the Old Testament Law that were never rescinded nor commanded. Christians have been debating those rules ever since. However, if you read the New Testament carefully, you will at least find that the Ten Commandments are all still in force, since at one point or another all of them are covered.
However, even those commandments that are still in force are to be looked at in a new light. You are not justified by following them. Instead, having trusted in Christ by faith, as a saved person under the instruction of the Holy Spirit, you will desire to follow them out of love.