I don't want to pooh-pooh modern pop. I appreciate that as well, but my personal favorite kind of music is guitar-based rock. I like grunge and garage bands and alternative music, but that's more my personal taste.
It's hard to really articulate what the parameters are that make one song parody-able and another song not, but if I can come up with a good enough idea for it, I go for it, and if not, then I have to move on.
I'm always a little leery about doing shows where I'm not the headliner because when I first started playing in 1982 I opened for Missing Persons and got pelted for 45 minutes. After that, I made the decision to headline no matter what, even if I was playing to seven people. I wanted people to be there to see me.
When I started out, I didn't feel like I was really accepted in the music or comedy communities, and I was somewhere on the edge, but now I feel like I'm accepted in both, which is extremely gratifying.
In fact, when I come up with an idea for a parody I try to resist the urge to Google the idea to see if someone has done it already because the answer is almost always, "Yes, of course they have, they've thought of it!"