Can you correct nulls with acoustic treatments.

Acoustic treatment can help but don't expect miracles. Good start, BTW.

These other frequencies can be harmonics or "half-harmonics" of the main frequencies. What I mean by the latter would be, for example, 100 and 150Hz. Start in the corners behind the speakers. If you want to try before you buy, hang blankets,towels, or futons pads and try the test again.

The worst room I ever heard had one 8' diagonal wall in the rear corner. It had two 300Hz nodes just in front and to the side of the listening position that were painful, even with music. I helped him get some materials for DIY tube and panel traps and that helped quite a bit, except aesthetically.

You might have to completely rearrange the room with the speakers on the long or short wall. The good news is you have lots of room to deal with and, apparently, bass is not the problem. It's easier to deal with higher frequencies.

I don't trust readings below 100 Hz for reasons of speaker and instrument inaccuracy. However, the dips centered around 125 and 250 Hz are definately room related. I would suggest focusing on those and hope for ancillary benefits below.

Playing those test tones, you should also be able to find the nodes by walking around the room, probably by ear. I would be willing to bet that there are two nodes parallel to the speaker plane. I mention this because it might lead to the easiest solution, by experimenting with speaker/trap location. Start with traps in the corner.

If you're ambitious, you can try DIY panel traps. There isn't much in the way of designs and plans available on the net but you'll get the vague idea with research. I built some using 1/8" hardboard for the panels. Some basics are covered online through the Sound On Sound articles, "Room for Improvement" (5 parts in DIY section). Geared toward studios and pros. At least, they aren't selling anything.