I'm not clear on what you are asking. Are you meaning to say that the 4 lights will total 120 WS (or each will be 120 WS). 120 WS for all 4 combined would be totally unacceptable. I have a 15 by 15 studio (more or less) and use 440 WS in 4 heads and that is enought to shoot at f8 with ASA 100 most of the time. So that is about the minumum power that one would need.
You mention the background will be lit by available light. Is that what you mean? Are you saying that you have a light source in the room that will always provide the light for the background. If so, then you'll have to use low shutter speeds if you want to have the background play an important part relative to its lighting.
As to lighting arangement that depends on what you are shooting. I normally only use one main and one fill and then use one or more of the strobes to light the background. A hair light is also useful.
Here is an example shot from my small studio:
This shot was lit with a large softbox to the left (about 45% left front). A fill light in umbrella was on the right about 45% left front. Then I had the other two strobes lighting the background and slanted so none of their light fell on the model. (440 WS distributed amoung the 4 heads with the main light set to be twice the level of the others - Novatron power pack).
Cheers,
Roger