This is a really good question. I think War Rooms are a huge benefit to any project especially when people outside of UX are also using it (business line managers, developers, IT, marketing, etc).

I've rarely seen it implemented well in a physical shared room, so it's likely going to be a challenge online.

One option that comes to mind is 37Signals Campfire tool...which is really just a group discussion room where people are sharing a constant stream of questions and critiques along with all sorts of visuals. We use something similar, but sans pictures, so, not nearly as useful.