For me the strangest thing of all, because I can't understand how it can be true, and yet I firmly believe in it, is free will. That we, some tiny specks on a planet, are free, when almost all the other matter in the universe is merely reactive. Incredible.
But leaving aside those sort of philosophical 'strange things', I suppose the strangest concrete thing I believe is that aliens exist. I think it's unlikely we are the only living things in the universe, and yet how strange to think there are other lives out there.
What is the strangest thing you believe?