First, what is the law being written about in Romans 3:31?
The whole chapter and its context must be grasped. Paul has been building up the case for God showing no partiality between Jews and Gentiles. God will judge the world impartially. On what basis? That everyone is under sin (vs. 9). Whatever the law says, it says to all who are under the law, and as both Jews and Gentiles alike stand condemned as law-breaking sinners, they will all be silenced before the Judge of all the Earth who will find them guilty. That is what the perfect law of God does. Nobody can keep it; everyone breaks it, therefore the law condemns everyone as unrighteous - 1 Timothy 1:9. And, as Paul says a few verses before the verse in question:
"Therefore by the deeds of the law there shall no flesh be justified
in his sight: for by the law is the knowledge of sin. But now the
righteousness of God without the law is manifested, being witnessed by
the law and the prophets; even the righteousness of God by faith of
Jesus Christ unto all and upon all them that believe. For there is no
difference, for all have sinned and come short of the glory of God."
Romans 3:20-23 K.J.
That makes clear, then, that believers who have faith in Christ do not make void the perfect law of God. Faith actually establishes it - as what? As being one of the two witnesses that establihes the righteousness of God by faith of Jesus Christ to all who believe. The second witness is the prophets.
Second, what is the law being written about in Ephesians 2:15?
It is clearly stated to be "the law of commandments, contained in ordinances". So, what does that verse say about that? Why, that it has been abolished in Christ's flesh. But it says a bit more that must not be missed out! What Christ achieved in his flesh resulted in the enmity against God by Jews and Gentiles being abolished (that enmity being the law that none of them could keep). Now peace could join believing Jews and Gentiles together, finally reconciled to God through what Christ achieved by the cross. The enmity was gone. Christ took it away by the perfect sacrifice of himself.
That is how "the righteousness of God without the law is manifested", "even the righteousness of God by faith of Jesus Christ unto all and upon all them that believe." That's the Romans 3:20-23 bit again.
It has now be shown what the "reconciliation" is that Paul refers to.
There is no need to wonder if the problem has been a different meaning of "abolish (katargeo)" or a different meaning of "law (nomos)." No. There is nothing wrong with the use of those words. Because reconciliation has been achieved, the law has served its purpose - Christ has fulfilled it so that it has, indeed, served to lead to the reality - Christ. It was only ever the shadow. Believers have stepped away from the shadow to live holy lives in faith of Christ, reconciled to God. They are at peace; new creatures in Christ - Colossians 2:10-17.
Making the law void is one thing, and annulling it is quite another. Christ was the fulfillment of the law. He never made it void. But a marriage is annulled when one party dies, and then the will (testament) of the deceased comes into effect. Jesus died in the flesh, thereafter the new testament in his blood came into effect. Release from the condemnation of the law, and inheriting the new covenant in his blood took place. Hebrews 8:13 to 9:1-17 gives all the details for that, showing what the reconciliation is all about.