The sons of God
The 'sons of God' who take wives among the daughters of men — fallen angels (with Jude 6), the line of Seth, or ancient rulers.
Genesis 6:1-4
1When men began to multiply on the surface of the ground, and daughters were born to them,
2God’s sons saw that men’s daughters were beautiful, and they took any that they wanted for themselves as wives.
3Yahweh said, “My Spirit will not strive with man forever, because he also is flesh; so his days will be one hundred twenty years.”
4The Nephilim were in the earth in those days, and also after that, when God’s sons came in to men’s daughters and had children with them. Those were the mighty men who were of old, men of renown.
What each tradition says
Rabbinic / Midrashic
Hirsch notes that the fall is narrated especially of Samḥazai and Azael. In Targum Pseudo-Jonathan to Genesis 6:4 they appear as the “nefilim” (A.V. “giants”), undoubtedly because this word was incorrectly interpreted as “those that fell from heaven.”
Emil G. Hirsch (1851-1923), The Jewish Encyclopedia, vol. 5, s.v. 'Fall of Angels' (New York: Funk & Wagnalls, 1901-1906) — Opening section, on Samḥazai and Azael and Targum Pseudo-Jonathan to Genesis 6:4
Rabbinic / Midrashic
Rabbi Shimon ben Yoḥai, when translating this verse into Aramaic, called them “the children of judges.” He used to curse anyone who would call them, translating literally, “children of god.”
Bereshit Rabbah, a saying of Rabbi Shimon ben Yoḥai; English: The Sefaria Midrash Rabbah, 2022, Bereshit Rabbah (Genesis Rabbah) — Comment on Genesis 6:2 (Bereshit Rabbah 26:5)
Patristic
Justin Martyr holds that the angels transgressed God’s appointment. Captivated by love of women, they begat children, and those children are the ones called demons.
Justin Martyr (c. 100-c. 165), The Second Apology (trans. A. Cleveland Coxe), in Ante-Nicene Fathers, vol. 1 (Buffalo: Christian Literature Publishing Co., 1885) — ch. 5 ('How the angels transgressed')
Patristic
Augustine says the sons of God were, according to the flesh, the sons of Seth. According to the Hebrew and Christian canonical Scriptures, there were many giants before the deluge, citizens of the earthly society of men. The sons of Seth sank into that community when they forsook righteousness.
Augustine of Hippo (354-430), The City of God (trans. Marcus Dods, 1871), in Nicene and Post-Nicene Fathers, ser. 1, vol. 2 (Edinburgh: T&T Clark, 1887) — Book XV, ch. 23
Catholic
Aquinas, quoting Augustine, says God's holy angels could not have fallen before the deluge. So the sons of God are the good sons of Seth, and the daughters of men are from Cain's race. Giants born of them are not surprising: not all were giants, though more existed before the deluge than after.
Thomas Aquinas (1225-1274); trans. Fathers of the English Dominican Province (1920), Summa Theologiae, Prima Pars (New Advent edition) — Ia, q. 51, a. 3, Reply to Objection 6 (quoting Augustine, De Civitate Dei XV)
Orthodox
No sourced position found. Checked John of Damascus, An Exact Exposition (no treatment of Gen. vi. 1-4), Basil's Hexaemeron (ends at the creation of man, Gen. i.), the 1672 Synod of Jerusalem (no relevant article), and the East's classic reading in Chrysostom's Homilies on Genesis 22, which has no public-domain English translation (Robert C. Hill, FOTC 82, 1982, in copyright; archive.org copy lending-restricted). No public-domain English Orthodox statement specific to this passage was found.
Reformed / Protestant
Calvin says Moses does not distinguish the sons of God from the daughters of men by nature or origin. Rather, the sons of God were those adopted by God and set apart for himself, while the others remained in their original condition.
John Calvin (1509-1564), Commentaries on the First Book of Moses Called Genesis, vol. 1 (trans. John King; Edinburgh: Calvin Translation Society, 1847) — Commentary on Genesis 6:2
Evangelical
Wesley takes the sons of God to be those called by the name of the Lord, the posterity of Seth. They did not keep to themselves as they ought but intermingled with the race of Cain, the profane daughters of men who were strangers to God.
John Wesley (1703-1791), Explanatory Notes upon the Old Testament (1765; CCEL's 'Wesley's Notes on the Bible') — Note on Genesis 6:2