It's a mistake to assume the gods are supernatural - this is not the case for all theologies. It's probably a safe assumption if you live in a culture dominated by classical monotheism, granted, but with the waning power of classical monotheist traditions even in places like the United States, tempering those expectations is probably a good idea. The only common denominator I've noticed in god-concepts throughout human cultures is that gods are that which are greater.
Which, clearly, is why those who accept the gods often invoke them when things happen - the gods are the higher powers that make things happen. Which gods and to what degree will depend in the tradition. Some theological traditions posit a very non-interventionist understanding of their higher powers (i.e., deism). Other theological traditions feel the gods keep a sort of "cosmic justice" that is beyond human understanding, rewarding the worthy and punishing the unworthy. Others still understand the gods to be diverse in form and motive, conflicting with one another in ways that is very consistent with the complexities we observe in the world (i.e., polytheism). And then there are the theological traditions that understand the greater powers to be the universe itself and so all things that happen are of the gods in some fashion or another (i.e., pantheism). There are many ways humans understand and relate to that-which-is-greater than themselves.
Personally, I certainly belong to a tradition for which signs and portends are relevant. In Druidry, there is a concept called Awen, which may or may not be deified but is something of a higher power in that it is the inspiration that moves us and calls us into action. It's that moment when an artist gets struck by a tune for a new song, or the time when you feel pulled to go on a walk outside to experience nature but don't really know why, exactly. When you let it flow, magical moments often happen that are very fulfilling and meaningful. Cultivating Awen and being open to inspiration no matter what the source is a major point of emphasis in the Druid order I belong to. To talk about it like it's a bad thing is a little bit baffling to me, but angstheists gonna angstheist.
