You probably want a little reverb, then a light distortion or a modulator effect, then a light flange or phase effect. Maybe the flange before the distortion, but you're going to want to play around with multiple combinations to get it just right.
You could also do an EQ (Equalizer) that cuts the frequencies above and below the range of the device you're trying to emulate, or in this case (a fictional device) the closest thing to it. Police radio, telephone, AM Radio, etc. The frequencies are easy to find online and once you look at the EQ in Audacity or a similar sound editing program you'll be able to turn some up and some down. Sometimes there is a graphic display for this and you can drag part of the spectrum up or down, sometimes you enter the actual values and don't get a visual representation, but it should work the same as long as it's EQ.
All these effects are available in Audacity and there are a lot more too, it's worth toying around with to get some ideas of what is possible. You can probably blend your sound a lot better than in Ridiculous Menace with some of the time/pitch stretch stuff and some noise reduction for bleeding music.
