Who is Oscar\'s Father?

First off, it's not Louis Tully. Oscar is not the by product of Zuul and Vinz Clortho mating. There is five years between the movies. Oscar is about eight months or so old in GB2. Basic biology says that's impossible

The real answer has never been 100% established onscreen or in any officially endorsed materials, but Sigourney Weaver (1989 on The Arsenio Hall Show) and Joe Medjuck (in the 1999 Ghostbusters DVD) both state, however, that Oscar's father is the violinist seen with Dana in one scene in GB1, whom Venkman calls "The Stiff" (and Sigourney referred to as "Mister Nose Spray").

He's never given a name onscreen (he's simply referred to as "Violinist" in the GB1 credits), but in the GB1 novelization he's referred to as Andre Wallance, which indicates that Dana's son's birth name is presumed to be Oscar Wallance