What are the Gods?
I would like to propose an answer that is not a unique or radical viewpoint, at least according to many Asatruar to whom I have spoken. Some may very well disagree with what follows, but it is a legitimate point of view within our religion.
The view is that the Gods are what I would call 'dynamic archetypes'. They are Beings that exist within and through us both as individuals, but especially en masse. An analogy would be that of comparing us to cells in their bodies. Unlike the static universal Jungian archetypes, they are more akin to the entities conjured up in a Ouija game - but in our case the 'game' is one played by the Northern European peoples over millennia.
This means that they can, and do, interact with individuals as well as entire societies. It also means that we cannot grasp the totality of the Gods due to their extent in time and space, nor are we often even aware of their plans and effects in the world. They operate on timescales far larger than individual lives, and have a 'long view'.
The Gods act as our interpreters, guides and exemplars to the ultimate mysteries of existence in all ages, and both define, and are defined by, the core elements of our culture. In addition, they also act as personifications of aspects of primary Human concerns, of Nature, and of their interaction. Hence as we come to know more of Nature and the way the world works, so we not only know the Gods to a deeper extent, but we enhance the depths of the Gods themselves.
This is consistent with a major mission of Odin - his search for knowledge. In fact, this analysis of the Gods leads to many predictions, which are addressed elsewhere.
As to what may be the 'ultimate mystery' that they show us, I would posit that it is named in our Lore as 'Wyrd' - the interconnected web of existence linking past, present and future. Certainly its equivalent, 'karma', in the other great Indo-European religions tends to underline this view. So, if we do have anything remotely resembling a 'God' in the recent sense of the word, it is an impersonal God that is the underlying unity of all things.