Outside of Paul, νόμος is used - almost always - to refer to sacred writings in the Old Testament.

Matthew always uses νόμος to refer to sacred writings in the Old Testament.
In Matthew 5:17-18 (English | Greek | Cf. 7:12; 11:13), “law” is not only used in synonymous parallel with “Law or the Prophets,” but also the “not an iota, not a dot, will pass from the Law” indicates that “the Law” refers to the Old Testament, which was translated into Greek (the alphabet of which includes the letter “iota”). The “law” that is “read” includes Numbers 28:9-10 and 1 Chronicles 9:23 - according to Matthew 12:5 (English | Greek). In Matthew 23:23 (English | Greek), the “law” is said to include matters weightier than tithing, a command from Deuteronomy 14:22.

John always uses νόμος to refer to sacred writings in the Old Testament.
Actually, most of the occurrences of νόμος are used in connection with Old Testament quotations. John 10:34 (English | Greek) quotes Psalm 82:6 “written in your law.” John 15:25 (English | Greek) quotes Psalm 35:19; 69:4, “written in their Law.” John 8:17 (English | Greek) refers to the requirement for multiple witnesses, a requirement which can be found in Numbers 35:30. John 18:31 (English | Greek | Cf. John 19:7) refers to the command to execute blasphemers, a command which can be found in Leviticus 24:10-16. John 7:51 (English | Greek; Cf. John 7:19, 23, 49) refers to the requirement for a hearing, a requirement which can be found in Deuteronomy 1:16; 17:6; 19:15; cf. Proverbs 18:3, 17. Finally, I do not know the Old Testament reference for John 12:34 (English | Greek).
In the remaining occurrences, John 1:17 and 1:45 use νόμος in connection with Moses.


Hebrews uses νόμος - almost always - to refer to sacred writing in the Jewish Bible.
The “commandment in the law” (ἐντολὴν… κατὰ τὸν νόμον) in Hebrews 7:5 (English | Greek) refers to a command to tithe to Levites found in Numbers 18:21, 26 and 2 Chronicles 31:4-5. Hebrews 10:28 (English | Greek) states that the verdict of guilt in breaking “the law of Moses” will be determined “on the evidence of two or three witnesses,” which can be found in Deuteronomy 17:6 and 19:15. Hebrews 10:1 (English | Greek | Cf. Hebrews 9:22; 10:8) refers to “the same sacrifices that are continually offered every year,” which can be found in Leviticus 16:34.


Other occurrences of nomos in Hebrews do not specify Scripture, but most likely do refer to Scripture. Hebrews 9:19 (English | Greek) uses the phrase “every commandment of the law” to refer to what Moses read from the Book of the Covenant, a reading described in Exodus 24:3-11. Also, consider Hebrews 7:12, 16, 19, 28; 8:4 (English | Greek).


Finally, in two verses, Hebrews may use it to refer to something other than Scripture, but, even, if so, the “my laws into their minds” of Hebrews 8:10 (English | Greek) and the “my laws on their hearts” of Hebrews 10:16 (English | Greek) are unlikely to refer to something contrary to what Scripture requires (cf. Romans 2:14-15, 23, 25-29; 3:27-28, 31; 7:21-23, 25 English | Greek).



James uses νόμος to refer to sacred writing in the Bible.
While James 1:25 (English | Greek) and 4:11 (English | Greek) do not provide clear clues as to James’ meaning from the word, James 2:8-12 (English | Greek) not only mentions “royal law according to the Scripture,” but also inserts a statement found in Leviticus 19:18 (which is also quoted by King Jesus in Matthew 5:43, 19:19, 22:39, Mark 12:31, and Luke 10:27) as well as two statements from Exodus 20:13-14.



Luke always uses “law” (νόμος) to refer to the Old Testament.
Most occurrences refer clearly to the Old Testament. Luke 16:16-17 (English | Greek | Cf. Luke 2:27, 39; 24:44; Acts 13:15; 24:14-15; 28:23), “Law” is not only used in synonymous parallel with “the Law and the Prophets”, but also the “dot of the Law” refers to a dot on a page. After people in the synagogue were “reading from the Law and the Prophets,” Paul is quoted as giving the next occurrence of the word with “law of Moses” in Acts 13:15, 39 (English | Greek | Cf. Acts 7:13-14; 28:23). Removing any doubt, Luke 2:22-24, 27, 39 (English | Greek | Cf. Acts 15:5) quotes loosely from the following passages: Exodus 13:2, 12 and Leviticus 12:8, which are “according to the Law of Moses” and “in the Law of the Lord.” For Acts 23:3 (English | Greek), English Standard Version suggests a cross reference with Deuteronomy 25:1-2, which could fit - if we remember that a hearing was necessary prior to the punishment (Deuteronomy 1:16; 17:6; 19:15; cf. Proverbs 18:3, 17).
Other occurrences refer more subtly to the Old Testament, associating “law” with Jews (Acts 18:13-14; 21:20, 24, 28; 22:3, 12; 23:29; 25:8), as well as angels (Acts 7:53).


Paul uses νόμος to refer to sacred writing in the Old Testament.
Most of the occurrences of νόμος in Paul refer to sacred writing in the Old Testament.
Paul uses “law” and “Scripture” interchangeably.
1 Corinthians 9:8-9, 20 (English | Greek | Cf. Deuteronomy 25:4) answers a question about “the Law” with what “is written in the Law of Moses,” offering a particular statement found in Deuteronomy 25:4
As a parallel, 1 Timothy 5:18 (English | Greek) quotes the same statement, but describes its source as “Scripture,” not the “the law.”
Paul does use “law” clearly to refer to sacred writing in the Old Testament. In Romans 7:6-9 (English | Greek | Cf. Romans 7:1-5, 12, 14, 16), “law” is used in synonymous parallel with “the old way of the written code,” and what the “law had… said” is a quotation from Exodus 20:17 and Deuteronomy 5:21. Romans 3:19-21 (English | Greek) uses “law” (νόμος) in synonymous parallel with “the Law and the Prophets.” In Romans 10:4-5 (English | Greek | Cf. Ephesians 2:15), “Moses writes” and “law” are associated with “the person who does the commandments shall live by them,” which can be found in Nehemiah 9:29, Ezekiel 20:11, 13, and 21. Galatians 3:10-12 (English | Greek) includes three statements - that it associates with “law” (and, in one case, “the Book of the Law,” perhaps, referring to Deuteronomy’s preceding text) - that can be found in Deuteronomy 27:26, Habakkuk 2:4, and Leviticus 18:5; Galatians 3:13 (English | Greek) connects “from the curse of the law” with what “is written,” which is the following: “Cursed is everyone who is hanged on a tree.” 1 Corinthians 14:21 (English | Greek) follows “[i]n the law, it is written” with words from Isaiah 28:11-12; the “law” a few verses later in 1 Corinthians 14:34 (English | Greek) most likely refers to Genesis 2, because Paul uses the same Greek words to mention women speaking as “not permitted” in contrast to their “submission” in 1 Timothy 2:11-12 - before rooting his command’s legitimacy in the story in Genesis 2.
But Paul also uses “law” more subtly to refer to the Old Testament, associating “law” with the Jews in Romans 2:12-15, 17-18, 20, 23; Philippians 3:5-6, 9; 1 Corinthians 9:20 (English | Greek), as well as with God in Romans 6:14-15; 8:3-4, 7 (ESV | Greek) and with timing congruent with the coming of the Old Testament in Romans 4:13-16; 5:13, 20 (English | Greek). Also, in Galatians 3:17-19, 21, 23, 24; 4:4-5 (English | Greek), the sequence of events in regard to νόμος is congruent with the timing of the coming of the Old Testament. In the context of the sequence Galatians 3:23-24; 4:4 (English | Greek) of the law “before faith came” and “until Christ came” - who was “born under the law,” it is reasonable to perceive references to the Old Testament in the usage of “law” and “works of the law” in contrast with “faith in Jesus Christ,” “God,” and “Spirit” in Galatians 2:16, 19; 3:2, 5; 5:3, 4 (English | Greek | Cf. Galatians 2:21; 4:21; 1 Corinthians 15:56), especially since Galatians 5:3 (English | Greek) - in the midst of this contrast - also associates “law” with “circumcision,” which is a command in the Old Testament (as Paul’s coworker makes obvious in Luke 2:22-24, 27, 39, where he quotes from “the Law of the Lord”).
In Romans 9:31 (English | Greek), Paul is referring not to the written code of works, but to the “righteousness by faith” described in the Old Testament about Christ - specifically, in the quotations in 10:6-9.

However, following the context of references to the Old Testament, occurrences of “law” are included as references to something not necessarily identical to the Old Testament - but, perhaps, instead, the goal of the law. In Galatians, Paul shifts from using the law to refer to the Old Testament in Galatians 5:14, 18, 23; 6:13 (English | Greek), where he describes what fulfills the “law,” a word that is modified as “the law of Christ” in Galatians 6:2 (English | Greek). In Romans as well, Paul describes what fulfills the law in Romans 13:8, 10 (English | Greek).
In Romans 2, obeying the written code is in contrast to obeying what the law requires (which has been written on your heart, by the Spirit).
Romans 2:14-15, 23, 25-29 (ESV | Greek). 14 For when Gentiles, who do not have the law, by nature do what the law requires, they are a law to themselves, even though they do not have the law. 15 They show that the work of the law is written on their hearts, while their conscience also bears witness, and their conflicting thoughts accuse or even excuse them… 23 You who boast in the law dishonor God by breaking the law. … 25 For circumcision indeed is of value if you obey the law, but if you break the law, your circumcision becomes uncircumcision. 26 So, if a man who is uncircumcised keeps the precepts of the law, will not his uncircumcision be regarded as circumcision? 27 Then he who is physically uncircumcised but keeps the law will condemn you who have the written code and circumcision but break the law. 28 For no one is a Jew who is merely one outwardly, nor is circumcision outward and physical. 29 But a Jew is one inwardly, and circumcision is a matter of the heart, by the Spirit, not by the letter. His praise is not from man but from God.

Romans 3:27-28, 31 ESV | Greek
27 Then what becomes of our boasting? It is excluded. By what kind of law? By a law of works? No, but by the law of faith. 28 For we hold that one is justified by faith apart from works of the law…. 31 Do we then overthrow the law by this faith? By no means! On the contrary, we uphold the law.


In Romans 7, not obeying the written code is in contrast to obeying the law of sin (which, I suppose, is written on your heart as well).
Romans 7:21-23, 25 ESV | Greek
21 So I find it to be a law [τὸν νόμον] that when I want to do right, evil lies close at hand. 22 For I delight in the law of God, in my inner being, 23 but I see in my members another law [ἕτερον νόμον] waging war against the law of my mind and making me captive to the law of sin [τῷ νόμῳ τῆς ἁμαρτίας] that dwells in my members…. 25 Thanks be to God through Jesus Christ our Lord! So then, I myself serve the law of God with my mind, but with my flesh I serve the law of sin [νόμῳ ἁμαρτίας].


In Romans 8, obeying the law of the Spirit (on our hearts, right?) is in contrast to obeying the law of sin and death.
Romans 8:2 ESV | Greek
For the law of the Spirit of life has set you free in Christ Jesus from the law of sin and death.