OK So I was just thinking that it felt weird to suddenly introduce vampires into Paranatural. Paranatural has it's own mythology, and internal logic. It has established Ghosts, Spirits, and Spectal Energy. It has also established rules which govern these things. But it hadn't established other supernatural things like vampires, so suddenly introducing vampire lore feels weird, but it would feel less weird if there were an explanation that linked it back to the Paranatural-specific lore.
So THIS IS THE THEORY: Cody's dad is a Medium for a Spirit which grants him vampire traits. We know that spirits can lend mediums their powers, and that the Medium gradually looks more like the Spirit over time. So, a Spirit with a big weird chin, fangs, pale skin, aversion to sunlight etc.
In addition, the hook hand could even be a Tool possessed by a Spirit with spatial warping powers. We know that it's possible for one person to control multiple spirits, although it can be difficult to do so. I could see a vampire being able to master such things, and it would bring a much needed explanation to what this new character has been able to do.