Alright, I've put this down on some protoboard. Lesson learned here: stripboard is sometimes easier - solder bridges are much harder to make intentionally. And solid core wire breaks if you bend it too much. Good things to learn. I managed to blow up my LM7824 regulator and so I had to head out to the electronics store to get a new one. It seems to be better.
I have images of my board for people to look over and catch errors and also as an example (perhaps of what not to do) for the benefit of fellow beginners who might see this in the future.
Top of the board. The wires sticking out are where I clip the power, source, and headphones.
Bottom of board. I've cleaned the rosin with alcohol. The leads to some components aren't clipped since I was swapping components in and out. I also used 'S'-jumpers for those interested.
So, on to my testing. Tangent, I don't know if this is because it's now on protoboard or because I put in a new regulator but that funky voltage imbalance thing that happened when I plugged into my computer disappeared! Genius you are. I was very excited, but noticed a hiss in the headphones when I had them plugged in. So I went off reading some more troubleshooting stuff.
First thing I did was lower the gain down to 3 (4.7k resistor). The hiss was still there, along with an awful crackle. There was also clipping at a very low volume. So out those resistors came and in went 2k resistors to put the gain up to 6. This eliminated the crackle and clipping, but not the hiss. So next up was the resistor on the output (R8 and R9 in my schematic). I had a 100 ohm resistor from another project, so I put that in (lowest value I had). Still a hiss. I reread Tangent's troubleshooting page and decided to put 100 ohm outside the feedback loop. Hiss gone!
What are the disadvantages of the resistance outside the loop? "[B]ad side effects" are mentioned, but never elaborated on. Everything seems to be a bit quieter. Also, should I remove the 100 ohm resistor inside the feedback loop now that I see that the resistance outside the loop works?
Another thing: while measuring the amp's current draw, I looked carefully at the datasheet (http://www.ti.com/lit/gpn/opa2132). I noticed operating voltage is 2.5V - 18V. I'm putting 24V through it. That's probably bad. Should I change to an 18V regulator? I ask because when I unplug the source I get really bad buzzing (the stereotypical buzz you hear in movies when somebody plugs a guitar into an amp). I thought this might be an oscillating amp and the high voltage might be the cause.
Thanks for the help so far!