Kind of sounds like your interface is automatically switching from direct monitoring to input monitoring when recording starts, and various possible sources of attenuation (including possibly +4dBu vs. 10dBV line levels and balanced vs. unbalanced cables) are coming into play when input monitoring that are not present when direct monitoring.
SONAR doesn't support ASIO Direct monitoring, so I'm not sure how that automatic switch would be happening, but nothing else really makes sense.
One thing to check would be to plug your headphone into one of the synths and make sure it's not the synth that's changing volume in response to MIDI CC7 coming from SONAR's track volume setting or something like that.
EDIT: On re-reading, I'm starting to wonder if your getting some phase cancellation issue from having SONAR's output going to the mixer from the interface, and then being fed back to the interface by the output of the mixer. In general it can be problematic to use a mixer to manage both input and output signals to/from your interface as it sounds like you are doing. I've done it to take advantage of the mic preamps on my Mackie, but you have to be very careful how you have things set up, and I would never route the monitor outs back to my interface directly.