+1 to what both SAC and DanDan said.
I can't make it out very well from the cool panorama, but I would guess the sidewall separation and the floor-ceiling dimensions are very close to each other.
You need to start measuring. Get the dimensional information of the room. Then start measuring the problem frequencies. Like DanDan said, a signal generator and your ears (or a simple sound level meter), will tell you the basics. REW will get you a lot more information to work with.
It seems apparent that you have strong room mode issues, especially being that you have little to no bass trapping. Any room of that size is guaranteed to need large amounts of bass trapping of some form. Remember, bass traps can actually increase the bass you hear. It seems counter-intuitive, but trapping bass can can actually increase the bass. You need to stop the cancellation at certain wavelengths.
With the room dimensions you can use a room mode calculator such as
http://www.bobgolds.com/Mode/RoomModes.htm to figure out where the room where the primary room mode frequencies should be.
You have a lot of potential to get a lot more control of your room.
Nathan