I have always assumed they were Divine, in accordance with the views of Michael Heiser, but these websites suggest otherwise:
You suggest the choice is between "divine" and human. Generally speaking most scholars would not refer to them as divine. They are angelical beings and angels are not divine. In the Job references it is generally accepted that the reference is to angels, with Satan being included with them.
Biblical scholars have debated the phrase "sons of God" in Genesis 6 for decades. There are numerous variations that have been proposed. Generally the two main competing views are the following:
The sons of God are those who followed in the line of Shem and in reference to Genesis 6 they are those who marry and have children with the unbelievers, that are then punished. Most of the arguments in favor of this view center on the fact that it is argued that angels could not cohabitate with women. The arguments against this view are that the fact that if Moses meant the line of Seth it would seem likely that he would have spelled it out by name instead of a general phrase. It also introduces two meaning for the phrase based on the context (not a major issue but one nonetheless). This view also does not have an adequate answer to the Jude 6-7 issue to follow. One of the biggest weaknesses with this view is this appears to be a very unique set of circumstances based on God's reaction. If this had been ordinary men, then why did he punish them this time with such severity? It is likely that it had happened in the past and it certainly happened in the future and still does.
The alternative is that the Genesis 6 passage is referring to angels as well, who cohabitate with woman to produce of hybrid race that God punished and cast the angels into the bottomless pit. This argument is based on Jude 6, which describes angels who left their first estate, who "left their own habitation." Verse 6 of Jude does not describe the exact nature of leaving their first estate. Jude 7 begins with the comparative conjunction ὡς (even, like, as) which links Jude 7 as a continuation of verse 6, thereby suggesting that the sexual sins of Jude 7 are linked to previous verse. This then suggests that Jude 6 is describing angels who committed sexual sins. This interpretation then suggests that Genesis 6 is the previous explanation of this event. The strength of this view is it best explains why Jude would include the conjunction in Jude 7, it keeps the Old Testament usage more consistent. The weakness is the idea that angels could procreate with women. The uniqueness of the Genesis 6 event is also best explained by this view.
Since both interpretations have strengths and weaknesses this has been a long standing debate. I tend to favor the second view that Genesis 6 is referring to angels, based on Jude 6-7.