Titans

This is a surrejoinder to Bnonn's rejoinder: 

http://bnonn.com/how-many-sons-of-god-can-dance-on-the-head-of-a-pin/

To our knowledge, alternative readings are late innovations in the history of understanding the text. That lends prima facie weight to the traditional reading.

A problem with appealing to Second Temple literature is that, during the Intertestamental period, there's blatant syncretism between Gen 6:1-4 and Greek mythological cosmogony or theomachy. Some Jews assimilate Gen 1 6:1-4 with a war in heaven between the Titans and the Olympians:  

Not by youths was their champion struck down, nor did Titans bring him low, nor did tall giants attack him (Jdt 16:6, NABRE). 

For their hero did not fall at the young men's hands, it was not the sons of Titans struck him down, no proud giants made that attack (Jdt 16:6, NJB). 

And the allophyles came and converged on the valley of the Titans (2 Sam 5:18, cf. v22; LXX). 

Occupying the valley called that of the Titans (Josephus, Antiquities, 7:71).

And then afterward again
Oppressive, strong, another second race
375 Of earth-born men, the Titans. All excel
In figure, stature, growth; and there shall be
One language, as of old from the first race
God in their breasts implanted. But even these,
Having a haughty heart and rushing on
380 To ruin, shall at last resolve to fight
Against the starry heaven. And then the stream
Of the great ocean shall upon them pour
Its raging waters. But the mighty Lord
Of Sabaoth though enraged shall check his wrath,
385 Because he promised that again no flood
Should be brought upon men of evil soul (Sibylline Oracles, Bk. 1).

130 And then the generation tenth appeared
Of mortal men, from the time when the flood
Came upon earlier men. And Cronos reigned,
And Titan and Iapetus; and men called them
Best offspring of Gaia and of Uranus,
135 Giving to them names both of earth and heaven,
Since they were very first of mortal men.
So there were three divisions of the earth
According to the allotment of each man,
And each one having his own portion reigned
140 And fought not; for a father's oaths were there
And equal were their portions. But the time
Complete of old age on the father came,
And he died; and the sons infringing oaths
Stirred up against each other bitter strife,
145 Which one should have the royal rank and rule
Over all mortals; and against each other
Cronos and Titan fought (Sibylline Oracles, Bk 3).

Back to Bnonn:

If 2 Peter 2 and Jude are referring back to Genesis 6:1-4, as they appear to be…

There's nothing in the actual wording of 2 Pet 2 or Jude which either states or implies an allusion to Gen 6:1-4. 

We know next to nothing about the abilities of the sons of God, save that they are literally godlike.

They're "godlike" on Heiser's interpretation, but of course, that's not something I grant. For instance, in his commentary, Sailhamer thinks "sons of God" alludes to the immediate origin of Adam from God whereas "daughters of men" alludes to the mediate origin of Eve from Adam. One can debate that, but it has contextual merit. 

Under biblical anthropology, human beings are a composite of spirit and matter. Is there some reason—some definitive, scientific reason—that the sons of God could not form human bodies to inhabit, or take human bodies to inhabit, in much the way that demons inhabit people?

i) To begin with, the text doesn't say or imply that the "sons of god[s]) took possession of human males. 

ii) But let's  play along with that scenario for the sake of argument. Suppose a demoniac fathers a child. In fact, given the prevalence of possession at sundry times and places, it wouldn't surprise me if some mothers or fathers are demoniacs. 

Assuming, however, that you're the child of a demoniac, that doesn't make you a genetically-enhanced human being. You don't have an upgraded body because your father and/or mother was demonically possessed at the time you were conceived. Is the child of a demoniac a hybrid physical specimen? 

Mind and body are two distinct domains. At most, there'd be some psychological rather than physical transference. The child of a demoniac might be mentally ill, or have paranormal abilities (e.g. ESP, psychokinesis).