Sons of god were angels, daughters of men were women. When angels breed with mortal women, the result is mortal hybrids who are demi-gods. Needless to say, the seed of mortal men is needed to complete this process, but the added influence of the angels creates changes in the offspring that give them extraordinary abilities. All the heroes of the ancient world were the result of this coupling between mortal women and angels/gods/spirits -- whatever name you want to put on these beings.