As I mentioned in my discussion of the possible allied-color gold gods of Theros block, we have confirmation straight from Mark Rosewater that there will be another five gods each in Born of the Gods and Journey into Nyx. Whereas Theros brought five monocolor mythic gods, who preside over wide-ranging natural occurrences and hence have the greatest power over Theros, the ten multicolor minor gods have rather smaller and more specific influences.
Among the allied-color gods are the rulers of wisdom, dishonorable warfare, and agriculture. All of these are quite recognizable and universal societal pursuits. Most likely, the enemy-color gods will continue that flavor trend. Let's see who and what exactly those gods could be:
White-black: We don't have much to go on here, it seems, at first - no mention in the Planeswalker's Guides of any gods whose personalities really fit this color combo or anything like that. But there's a pretty big hint right there in Theros - Scholar of Athreos is part of the off-color-activation ten-card cycle in this set, and the Athreos in that name seems to be a person, not a place. That card's flavor text, and that of Sentry of the Underworld, make it clear that Athreos is a sort of Charon figure - the ferryman and judge of the dead. A very white-black notion, thematically similar to the Orzhov guild of the previous block but also quite different, and fitting of the concept of a god related to Erebos but not subordinate to him.
Black-green: This one is fairly a softball; it looks like the black-green god will be Pharika, sovereign of healing and venom, seen taking the form of a Gorgon in the background of Pharika's Cure, and definitely worshipped by black-green Gorgons such as Pharika's Mender. She looks like a very interesting character, quite distinct from the Golgari except with reference to the duality of her nature.
Green-blue: There's one crucial hint that points to who this is - Prophet of Kruphix seems to indicate that the green-blue god is in fact Kruphix, God of Time. Not much is known about this enigmatic and impassive god, and that one card seems to be the only mention of him so far. We can probably expect Temporal Spring-like shenanigans with him.
Blue-red: Compared to the other minor gods, references to Keranos, God of Storms, are all over the place. Queen Cymede, for example, is known to be a devotee. He's even name-dropped in the flavor text of Lightning Strike, and of Steam Augury just to press home the point of his color combination. Hell, the art of the former even features (the arm of) the god himself.
Red-white: And by process of elimination - and also by extremely obvious dint of portfolio - the red and white god must necessarily be Iroas, who rules over honorable combat. He's the good twin brother of the nasty Mogis, the patron of the red-white society of Akros and by extension its Olympics-like festival the Iroan Games, and makes a cameo appearance in the background of Priest of Iroas as a snazzy statue.