One of my vampires from Forgotten Hollow accidentally got infected by drinking from an infected. Other than that, I can’t remember ever seeing zombies in other worlds, unless of course you somehow turn your played sims into zombies yourself, as it happened to my vampire.
You can plant strange plants on lots in other worlds, but they won't grow in neighbourhoods outside of StrangerVille, and other strange occurrences such as the sky turning purple and tendrils coming out of bathroom appliances are restricted to StrangerVille as well.
If you want StrangerVille to be a completely normal world, you have to play through the story at least once. But other than that, the rest of your worlds shouldn’t be affected.