Genesis 6:4 is one of the most mysterious passages in the Bible. It has been open to a host of interpretations, however, those who hold consistently to a biblical worldview must reject the notion that women and demons can engage in sexual relations. They can not mix and produce fertile or any offspring at all. Despite this evident truth so many keep suggesting that we see in Genesis 6 the production of hybrid giants, yet several scriptures show this can not happen.
Remember that Jesus indicated in Luke 24 that spirits do not have flesh and blood bodies, which means also a lack of DNA. Spirits are also very limited in the ability to create, although they can certainly interact to various extents. I would suggest what we see in Genesis 6 is widespread demon possession and paganismin a very degenerate society. Demons can give knowledge and influence to men and make them mighty (gibborim) although evil at the same time. These would be the “giants” or “fallen ones”(nephilim) of old.
The “possession theory” may lack the luster of some theories but is Biblically more sound and truth is what we want.