Will you remain atheist even after becoming Asatru? That would be interesting, since the word "Asatru" means "Loyal to the Aesir".
Either way, from what little I can guess from a person coming from a Catholic family, my personal advice is this: monotheistic thinking and polytheistic thinking are very, very different. Far more different, in fact, that a lot of people realize. Understand that by "monotheistic/polytheistic thinking", I don't necessarily refer to a state of theistic belief. Monotheistic thinking permeates virtually all of Western Culture, even among those who are atheist. There are very few who have either made the transition to, or already had, polytheistic thinking. Conceptions like pluralism and tribalism are common here. We also do not hold fast to any book or text. Lore is dynamic and ever-shifting. A story highly relevant to one generation is barely remembered the next.
Understand that the Old Way, as I prefer to call it as a Modern English translation of the Old English term "forn sidu" (Old Norse "fyrn siðr)", is hidden not just in the obvious places like the Edda Lays, Icelandic Sagas, and Wagnerian Operas. You'll find them in the fairy tales collected by the Brothers Grimm, in the legends of Arthur and Robin Hood ballads, in the Finnish Rune Songs, in many of the songs we sang as children, and even in our very language. Sure a lot of these now have a Christian coat on them, but they still contain faint echoes of the Old Way.