Answer: The phrase "sons of God" is found five times in the Old Testament (Genesis 6:2, 6:4, Job 1:6, 2:1 and 38:7) and five times in the New Testament (Romans 8:14, 19, Philippians 2:15, 1John 3:1 - 2). It has three primary meanings in the Bible, only one of which is made in reference to angels. The other two uses of the "sons of God" references humans.
An example of the first primary meaning of "sons of God" is found in the Book of Job. It states that angels presented themselves before the Eternal and with them was Satan the devil (Job 1:6, see also 38:7). Clearly, the righteous spirit beings are being referenced as "sons" and not Lucifer.
A second usage of this "sons" phrase occurs in the King James Bible translation of the Book of Genesis. In the sixth chapter it states that certain people married women and together produced children who became giants, "mighty men" and "men of renown." The verse in question states, "And it came to pass, when men began to multiply on the face of the earth, and daughters were born unto them, that the sons of God saw the daughters of men that they were fair; and they took them wives . . ." (Genesis 6:1 - 2, KJV).
This phrase in Genesis 6:1 - 2 cannot be a reference to angels, either to those who are righteous or evil. The word of God does not contain even a hint that flesh and blood humans can somehow mate with spirit-composed beings! Although there are some parallels in pagan thought regarding this possibility, this concept of spirits cohabiting with humans is simply not taught in Scripture.
Proof that "sons of God" does not refer to any angels procreating with females and producing giants can be found in verse 2 of Genesis 6. The Hebrew word in this verse translated as the English phrase "took them wives" is the word commonly used to refer to marriage in in the Old Testament. Jesus clearly states, in the New Testament, that angels do not marry (Matthew 22:29 - 30). Only human beings were (and are) given the gift, by God, of not only being able to marry but also to reproduce (see Genesis 1:28, 2:18, 21 - 24, 3:16).
The third primary usage of "sons of God" is found in the New Testament as a designation for people, both male and female, who are in a covenant relationship with the Eternal (they are true Christians). It should be noted that humans are not automatically considered to be in this kind of familial relationship simply by virtue of their birth.
True sons (and daughters) of God are humans, not angels, who repent of their sins, accept Jesus as their personal Savior, and receive the Holy Spirit. Several Bible passages referencing converted humans as being a part of God's family including John 1:12, Romans 8:12 - 19, 2Corinthians 6:18, Philemon 2:15, Galatians 4:4 - 6, 1John 3:1 – 2 and others.
Righteous spirits are only considered "sons" in the sense that they were initially created to possess the same spiritual composition or essence as their Creator. Humans, on the other hand, though born with flesh, have a far greater potential than any angelic being. In fact, in the near future, converted humans whom God has resurrected from the dead will be given the responsibility of judging angels (see 1Corinthians 6:1 - 3).