First, get a calibrated microphone. They’re $25 to $100.
Dayton imm6 or
UMIK-1
That your dips are happening at multiples of each other testify to having a standing wave due to wall surfaces around 7 to 8’ apart.
Room EQ Wizard has a bass decay chart which will help you see the problems with more clarity. REQW is free, but I use OmniMic.
When you plug the speakers, you are reducing bass and reducing the chance of exciting the room modes. What’s happening is that the room is ringing, like a bell. If you play no bass, you won’t hear it, so it sounds better, but, bassless.
Make sure your bass traps are adequate.
GIK Soffit traps are among the best and least expensive below 200 Hz. If after placing you still have those nodes, then increase bass traps first. The better your bass traps the more chance of lifting the lows, clipping the highs AND getting a better response regardless of listening location. They are the enabling tech. for room equalization. If you can’t EQ, it’s because your room treatment isn’t enough.
After assessing that, add a miniDSP unit or equivalent. Don’t try for flat, I usually use about 1 to 1.5 db downward slope above 70 Hz. Works best for music and movies.
If you don’t haver enough traps you wont’ be able to lift the dips, but you should be able to clip the peaks. What you’ll see in addition to the 80 and 160 Hz dips are some massive peaks, like +20 dB. By lowering them you’ll get a more full bass experience. Again, the better the room treatment, the easier and better your EQ results.
Best,
Erik