Got it, okay thanks. The MSP-90 was originally designed as a multiband audio processor for (mainly) FM stations. There were two versions; single channel and stereo. The device is 600 ohms +4db line level in and out. As you've discovered, connecting a mic directly into the MSP90 won't work because a mic is typically 5,000-15,000 ohms -50db mic level out. The only way you could use this with a Radio Shack mixer, would be to connect the MSP90 at the output of the mixer and jack up the input of the MSP90 high enough to do some processing. As with most consumer devices, keep in mind that your mixer outputs -10db at 0VU, where as mentioned; the MSP90 is designed for +4db at 0VU.
Now something about the MSP90: The rub against the Harris MSP 90 back in the day, was the lack of decent peak control and it had a pretty poor signal to noise ratio (hiss) as compared with competing processors. Fast forward thirty years, and several of the old capacitors inside that MSP 90 have dried-up, degrading performance even more.
I'm certainly not suggesting you don't have fun playing around with the device and electronics in general. I completely encourage it. It's just that if you're serious with trying to produce something for radio, a podcast, web stream, etc., that you may be disappointed with the end result by using the MSP-90 as a voice processor. As you've already discovered, there are much better choices which already include good microphone preamps from DBX, which will get you closer to a clean, processed sound.
Good luck!