You may have to scroll down in Game Options to find the Neighborhood Stories section.
I think it's under Game Options > Gameplay and then scroll down.
That's for the global on/off toggle.
Settings for My Households, other households, and individual households can be found under Manage Worlds > Household Manager.
Do you mean that your empty houses were being filled, before you turned them into rentals to keep them empty? If households are moving into houses on their own, that means the Neighborhood Stories feature is on, and that "Move In" is enabled for those households.