We don't know. My personal theory is that she is a demigod like Shadow, but Neil never confirmed nor denied it. Her father acts somewhat like Odin, wandering every few years. Marrying a woman, living with her, getting wanderlust, moving, meeting and marrying another woman. Only he is Native American. He dismissively calls her halfbreed.
As for why she was having those dreams, if you read the relevant chapter things become slightly clearer. Right after Shadow wakes up from lightning bird dream, he gets a call from Wednesday and gets scolded by him, to the tune of "What is the point of hiding you in the middle of nowhere if you're going to do that and shine like a beacon?" . I think that everybody around the Shadow or connected with him shared the dream of lightning birds at the time he had his dream. In fact, I think there is a couple of sentences which implies that people complained of odd dreams the next morning.