Yes, this is indeed what the song volume is supposed to do. The quickest way to do it is to use a software that can write ReplayGain tags into the songs. Stage Traxx will read this tag during import and set the song volume to that value.
You can use Foobar2000 to do this both on Windows and Mac: https://www.foobar2000.org
Use the "Scan per file track gain" option to get the most even volume settings.
If you already imported your files, the quickest way to even out the volume is still to analyze the tracks in Foobar2000. It will print the detected volume settings on the screen. Then adjust your volume manually to the Foobar2000 values.