It would probably help to give us a little more description of the problem.
Is it the program material being played from the decks that is going up/down? Is it the difference between the vocals and the program music? Both?
Who is watching the board during the performance/recording? That person is supposed to be watching the levels and making adjustments to the mixer during the performance to counteract this. This is also why there are audio level COMPRESSORS to help rein-in dynamic fluctuations like these. But nothing beats a good set of ears/eyes/hands to keep on top of it all...
You have to be careful with compressors in a live scenario (ANY situation, actually), and they aren't a "magic fix", but they certainly make a sound mixer's job a bit easier when used judiciously.
And, yes there are "plug-ins" that can be used on your DAW recorder to do this. What plug-in to get depends on the recording program you're using. And, once again, this will have limited effectiveness, depending on the program material and the initial recording levels.

Even if the person working the live sound knows what he or she is doing (not often the case in school productions) and the equipment is good (even rarer) I would expect significant variations in the audio level of the various segments of the performance.

To get a good soundtrack, I would split the recording you have into segments with their own audio characteristics. Each spoken word segment, solo song, and production number gets its own segment. You could then mix each segment with its own settings for EQ, limiting, compression, and volume. For instance, you can use much tighter low and high pass filters on the spoken word parts to eliminate noise and focus on the vocals.

However, your question sounds like you were just hoping to do a quick and dirty version of this and put the whole recording through single set of processors. If so, I'd start with a limiter. Focus on the loudest segment of the recording and see how much you can limit it without it sounding like you are putting it through a fuzz box. You will probably want to put the whole thing through a high pass filter to reduce room noise. The low register musicians will hate you, but no one ever listens to their complaints. This might work, but your description of the raw recording leads me to doubt it.

The console is being operated to reinforce sound for the room, so it will not sound like it should. Maybe you should use room mics.

You might try recording via the aux sends (pre fader ideally) so that you can mix for the house and mix for the rocorder simultaneously.

Sheet has a point. Is the orchestra being amplified? If not, the desk will turn up the singing to be heard over the orchestra and leave the spoken passages at a lower level. Good luck.