The term whammy is actually vampire slang. It refers to the vampiric power of hypnosis. "Whammy" can be used either as a noun (to "put the whammy on" someone) or as a verb ("to whammy" them).
Vampires' ability to hypnotize humans was an integral part of the series from the very beginning of the pilot episode; and "whammy" was actually employed in reference to hypnosis in the episode "Only the Lonely". However, the term is generally associated with the new characters introduced in Season Three. In that context, "whammy" was first employed in Black Buddha, Part Two", when Screed advises Vachon to whammy Tracy Vetter so that she will not remember that he is a vampire.