The following contains possibilities arising from scripture with veiled meanings. There is no suggestion that there is full scriptural backing for all the arguments at this time, although some of them seem pretty solid.
Various texts in the bible refer to "The Sons of God", others to the "Daughters of men".
Gen_6:2 That the sons of God saw the daughters of men that they were fair; and they took them wives of all which they chose.
Gen_6:4 There were giants in the earth in those days; and also after that, when the sons of God came in unto the daughters of men, and they bare children to them, the same became mighty men which were of old, men of renown.
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.
Job_2:1 Again there was a day when the sons of God came to present themselves before the LORD, and Satan came also among them to present himself before the LORD.
Job_38:7 When the morning stars sang together, and all the sons of God shouted for joy?
It is clear that the term "Sons of God" does not refer, in the Old Testament, to humans. They clearly are spirit in nature and Satan was among their company. The Hebrew word for "among" is translated many more times as "in the midst" so indicating that Satan was present as a member thereof, not as an intruder. Therefore, "The sons of God" were angels, probably including fallen angels because we are told that some angels are permanently very close to God, possibly implying that other angels are not.
Mat 18:10 Take heed that ye despise not one of these little ones; for I say unto you, That in heaven their angels do always behold the face of my Father which is in heaven.
Whilst Angels are clearly Spirits, they do have the power to assume human form, in which their physical bodies would include all the physical abilities and requirements of a human.
Gen 19:1 And there came two angels to Sodom at even; and Lot sat in the gate of Sodom: and Lot seeing them rose up to meet them; and he bowed himself with his face toward the ground;
Gen 19:2 And he said, Behold now, my lords, turn in, I pray you, into your servant's house, and tarry all night, and wash your feet, and ye shall rise up early, and go on your ways. And they said, Nay; but we will abide in the street all night.
Gen 19:3 And he pressed upon them greatly; and they turned in unto him, and entered into his house; and he made them a feast, and did bake unleavened bread, and they did eat.
In the New Testament "Sons of God" takes on a new meaning, being a state to which humans (true believers) attain. possible replacing that Old Testament category just as the Church replaces the Israelites as Abrahams seed.
Gal 3:29 And if ye be Christ's, then are ye Abraham's seed, and heirs according to the promise.
Joh_1:12 But as many as received him, to them gave he power to become the sons of God, even to them that believe on his name:
Rom_8:14 For as many as are led by the Spirit of God, they are the sons of God.
Rom_8:19 For the earnest expectation of the creature waiteth for the manifestation of the sons of God.
Php_2:15 That ye may be blameless and harmless, the sons of God, without rebuke, in the midst of a crooked and perverse nation, among whom ye shine as lights in the world;
1Jn_3:1 Behold, what manner of love the Father hath bestowed upon us, that we should be called the sons of God: therefore the world knoweth us not, because it knew him not.
1Jn_3:2 Beloved, now are we the sons of God, and it doth not yet appear what we shall be: but we know that, when he shall appear, we shall be like him; for we shall see him as he is.
However, it is clear that the "Sons of God" were able to have Earth bound children by the "Daughters of men" even though Jesus tells us
Mat 22:29 Jesus answered and said unto them, Ye do err, not knowing the scriptures, nor the power of God.
Mat 22:30 For in the resurrection they neither marry, nor are given in marriage, but are as the angels of God in heaven.
Jesus clearly says that this subject is revealed in the Scriptures. As far as I can see, He must have been referring to the "Sons of God" passages which reveal that conception takes place in the earthly environment. Also, bearing in mind that no female names are recorded for angels it would appear that once our spirits return to the Lord, we all lose our physical, sexual identity. We are all "As the angels of God in Heaven". How is that for perfect sexual equality!! Remember that God created man from dust to be "inhabited" by a spirit but woman from a part of Man - the piece near to his heart. In fact, protecting his heart and specifically to be his helper.
Gen 2:18 And the LORD God said, It is not good that the man should be alone; I will make him an help meet for him.
The involvement of the "Sons of God" with the "daughters of men" continued after the flood.
Num 13:33 We saw the Nephilim there (the descendants of Anak come from the Nephilim). We seemed like grasshoppers in our own eyes, and we looked the same to them."
because
Gen 7:21 Every living thing that moved on land perished—birds, livestock, wild animals, all the creatures that swarm over the earth, and all mankind.
Gen 7:22 Everything on dry land that had the breath of life in its nostrils died.
Referring to the coming flood
Gen 6:4 There were giants in the earth in those days; and also after that, when the sons of God came in unto the daughters of men, and they bare children to them, the same became mighty men which were of old, men of renown.
Note that this does not preclude the possibility that such relationships continue to day, unless the phrase "which were of old" means that time has passed.