How about using some software intended for the job?
"But how the hell can that be arranged and demonstrated?"
Strangely enough you're not the first to wonder what the data compression is doing to your audio. There is a great audio plugin by Sonnox that allows you to listen to an audio source via up to 5 streams simultaneously compressed through different codecs, bit-rates and depths, and switch between them. It's important to listen to bad encodings so that you can get a feel for the type of distortion you're looking for - once you can easily identify what mp3 artefacts generally sound like, it's much easier to spot them at higher bit rates.
I'm surprised that there's been little mention of AAC, since it's the default format on iTunes. I find MP3 artefacts are really noticeable and unmusical (when they are audible), whereas I generally find AAC just gets gradually softer and slightly muffled, which is far less apparent and invasive. A killer test for mp3 encoders is quiet hi-hats with reverb; It all turns into horrible swirly mush.
In terms of demo sources, it's possible to eliminate recording distortion effects altogether by using source material from pure synthetic instruments, like Pianoteq's Play, or most modeling synthesiser plugins, and you can then get audio source material that's never been though an ADC or DAC.