Although we are not under the Law we are not above it either, but rather we are more in tune with its spiritual components, a heart circumcised to believe and obey, trusting in Him and glorifying His name through our obedience; not being saved by it but being saved we fulfill it. Justification does not mean to be righteous or to make righteous but to declare righteous, for the Christian we are declared righteous based on the perfect righteousness of Jesus the Messiah. He has fulfilled the Law for us and by our faith we establish that fact.
The Law still has purposes, for the non-believer and also for the believer. It is designed to lead people to the gospel of Christ (Galatians 3:19-23) and also to indict what is not in accord with the gospel (Galatians 2:14). Using the Law lawfully (1 Timothy 1:8-9) means using it to convict people of living out of accordance with the gospel. It is for those that don’t know it and for those that should know better. That is why we use both, we give the Law to the proud and grace to the humble, both Christian and non-Christian.
Through faith or by faith means that our faith is not the ground or that we are saved on account of our faith, but that it is by grace through faith (Ephesians 2:8-9). God is absolutely holy and just, and so any justification, any declaration of righteousness, any acquittal of guilt, must be on a just basis; it must be right to do so. The penalty of the Law had to be satisfied and Christ paid that for us, and so God declares us righteous not on some whim, but because of Christ, and it is a just declaration. We are guilty but Christ pays the penalty, and then God is just in justifying the ungodly (Romans 4:5), declaring us righteous, because of the imputation of Christ’s righteousness to our account (2 Corinthians 5:21).
As we see in Romans 3:24-26, the substitutionary atonement is the reason we can be justified by faith. It is faith in the person of Jesus and His finished work on the cross. With the wonderful doctrines of substitutionary atonement and justification by faith you can rest assured of your salvation, and as you cling to Christ in faith, you can conquer those voices that tell you tomorrow morning that you are a hopeless case. You don’t have to remember the names of the doctrines to remember who and what they are about. Jesus Christ dying for your sins and giving you a right standing before a satisfied God. By abiding in Christ by faith, you are not above the Law; in Christ you have fulfilled it.