Recently, a topic came up that I thoroughly enjoy discussing, but about which there appears to be a lot of misconceptions. (This will in no way be exhaustive; many books have been written on these topics, and I hardly have the space to do a worthy study on them in a blog post!)
We begin our study in the usual place: at the beginning. (Note: all Scripture is from the King James Bible, and no authority other than It shall be appealed to, especially "The Greek" or "The Hebrew.")
Genesis 1:26 And God said, Let us make man in our image, after our likeness: and let them have dominion over the fish of the sea, and over the fowl of the air, and over the cattle, and over all the earth, and over every creeping thing that creepeth upon the earth.
The key word here is not what one would usually pick up on or make of any importance: the word to note is "image." Obviously, this verse supports the Triune nature of God ("our image"), and dually it speaks of man's triune nature as well: body, soul, and spirit. Adam was made in God's perfect image, a triune being, and certainly in the likeness of His physical appearance also.
As a result of that likeness and image, check out how Adam is referred to later:
Luke 3:38: Which was the son of Enos, which was the son of Seth, which was the son of Adam, which was the son of God.
Do note that in this instance, "son" is lower-case, denoting that Adam was not a deity: he was simply made in the image of God, and therefore was called the "son of God." Thus, the vast importance of the precise wording of John 3:16 is made apparent: Jesus is the only "begotten" son of God, or God the Son (capital "S"), so dropping the "begotten" (meaning God's direct progeny or "genetic" offspring) makes Jesus a liar, as there are many other beings that are called the "sons of God."
Now, we'll sally back to the first place in the Bible where the actual phrase "son(s) of God" is mentioned.
Genesis 6:1 And it came to pass, when men began to multiply on the face of the earth, and daughters were born unto them,
2 That the sons of God saw the daughters of men that they were fair; and they took them wives of all which they chose.
The typical argument here is that these "sons of God" are simply righteous descendants of Seth, as opposed to the unrighteous descendants of Cain. This is certainly a lousy exegesis, since Seth himself was said to have been born in Adam's image, not God's (Genesis 5:3). The fact is that when Adam sinned, he lost that perfect image of God: his spirit died. From that point on, man was unregenerate, fallen, and existed as a dichotomy: body and soul, with a dead, worthless spirit inside. Man's communion with God had been cut off, and from then on, man was born in the image of Adam (1 Cor. 15:49).
We'll conclude then, based on the evidence given in the book of Genesis, that the phrase "sons of God" cannot refer to human beings, since not only is there a precise distinction between God and mankind in this verse, but that indeed the image of God had been lost (and still is in unregenerate man). Therefore, these "sons of God" are something entirely different, and we'll look and see what the Bible says about them.
Job 1:6 Now there was a day when the sons of God came to present themselves before the LORD, and Satan came also among them.
Now, without getting into the Genesis 1:1-2 issue, let us simply state here that since it is the sons of God that are presenting themselves before God, and Satan is among them, that he is indeed numbered among these sons of God, though in an obviously fallen state. Why else would he show up? These are supernatural, angelic beings (Job 38:7) who were present at the creation, though Satan, among them, obviously no longer retains his office as the LORD's light-bearer (Ezekiel 28:14). These sons of God, then, are not based on their standing with God: they are called sons of God based on their creation (Genesis 6 details sons of God that were involved in vile sexual practices!). So far, we have established two things:
1. These sons of God are not human
2. These sons of God are supernatural, angelic beings who were present at the creation.
Now, let us tie together the different uses of "son of God" between the Old and New Testaments.
A serious student of the Bible will recognize that before Christ's death, burial and resurrection, there was no "new birth," no "Body of Christ," and no forgiveness of sins. As Christ was the "last Adam," (1 Cor. 15:45), he redeemed fallen man and restored the perfect Image of God (Rom. 8:29; 1 Cor. 15:49; 2 Cor. 3:18, 4:4; Col. 3:10)
With Christ's propitiation for our sins, He conformed us to the image of God through His death. We now have the power to become the sons of God, or regain that fallen image! The reason that a person or being is called a "son of God" is because he is made in the image of God, just as genetic children retain the image or likeness of their parents. In our case, as David said, we have been made a little lower than the angels (Psalms 8:5), but we have been given the unspeakable free gift of Eternal Life, something that the angels obviously don't have (Gen. 6, 2 Pet. 2:4, Jude 6).
Questions? Leave a comment and I'll reply to the best of my ability.