As PyRulez points out, the text from Moses 8:13-16 offers a larger perspective on what was actually going on in Genesis 6:
13 And Noah and his sons hearkened unto the Lord, and gave heed, and they were called the sons of God.
14 And when these men began to multiply on the face of the earth, and daughters were born unto them, the sons of men saw that those daughters were fair, and they took them wives, even as they chose.
15 And the Lord said unto Noah: The daughters of thy sons have sold themselves; for behold mine anger is kindled against the sons of men, for they will not hearken to my voice.
16 And it came to pass that Noah prophesied, and taught the things of God, even as it was in the beginning.
Joseph Fielding Smith in "Answers to Gospel Questions" 1:136-137 (search for the text "first two verses in Genesis, Chapter six") answers the question "Will you kindly explain the meaning of the first two verses in Genesis, Chapter six?" While I am not aware of the official canonicity of this publication, the answer to this question seems in line with the LDS canonized corpus as far as I can tell, and Joseph Fielding Smith was president of the church and I think was president at the time this book was written.
The full text of President Smith's answer is too long to include here in full. I will paraphrase and quote the most relevant points.
First he states that the notion that the "sons of God" as mentioned in Genesis 6:2 are heavenly beings who came down is false. (He actually calls it a "foolish notion [that] is the result of lack of proper information".)
President Smith then references Moses 8:13-16 as I have above. He uses these verses to establish that the "daughters of men" in Genesis 6:2 are actually the daughters of the sons of Noah. President Smith then offers this commentary:
Because the daughters of Noah married the sons of men contrary to the teachings of the Lord, his anger was kindled, and this offense was one cause that brought to pass the universal flood. You will see that the condition appears reversed in the Book of Moses. It was the daughters of the sons of God who were marrying the sons of men, which was displeasing unto the Lord. The fact was, as we see it revealed, that the daughters who had been born, evidently under the covenant, and were the daughters of the sons of God, that is to say of those who held the priesthood, were transgressing the commandment of the Lord and were marrying out of the Church. Thus they were cutting themselves off from the blessings of the priesthood contrary to the teachings of Noah and the will of God.
So, the answer to your question is that the use of "sons of God" in Genesis 6 is likely a mistranslation or some other error that occurred over the centuries, and according to Moses 8 the daughters of the sons of God (Noah's granddaughters) married the sons of men (men who did not have the priesthood).