I wouldn’t have thought the size of the deity would matter in oaths. Presumably both parties would be swearing oaths upon their own deity and would assume that the other person’s deity would be as powerful as their own in helping to keep the person from going against their words.
This may well have been the case, yet again the vagueness of details available frustrate us. I suppose the idea of the oath in this sense is less "with God as my witness" and more "on my honour" (and that of my god). I can understand my god punishing me for bringing his name into ill repute.
I may well be getting to "legal" about the hypothetical wording here but I guess it's relevant through my former post. Why would my god care if I betrayed an oath made to someone else if that person doesn't hold any respect in the eyes of my god, i.e. has never prayed or sacrificed to it. Using this odd logic it makes more sense to make an oath before the other guys god cause then you would fear retribution from an unknown who's got someone else's back not yours.
All of this is circumnavigated if there is a common or “big” that both parties recognise and will uphold both ends equally, supposing the god doesn’t have another personal reason to favour one party over the other.
And within the kin-based structure, where everyone has equal responsible for everyone else, the person making the oath would know that their own kin would be as much to blame as themselves with any oathbreaking.
The system of kin based accountability seems to be a perfect example of society being held together by familial bonds and mutual back scratching. While slightly elevated this may actually serve as evidence for a faith based on “smaller”, more local or less concerned gods.
Curiously, on the matter of people behaving better when they perceive themselves to be under the eyes of deities ; The New Scientist article did highlight that in secular societies with atheist majorities, (given example, parts of Scandinavia) The same effect achieved by religious word dropping to improve behaviour and sense of fairness can be brought about with secular words such as “civic, jury and police”. This combined with Kin group accountability becomes an incredibly effective deterrent to breaking laws/oaths.