I'd like to build a small internet radio out of my pi, but I'd like to use it at night, when the flashing LEDs would be disturbing. Is there any way to disable them?
Unfortunately not. The PWR LED, for example, is directly wired to the 5V rail and other LEDs are controlled by closed-binaries.
I know this may sound silly, but a piece of electricians tape over the top would work. Alternatively, put it in a case or box.
There is answer in How do I control the system LEDs using my software?
For Power led, if you have RPI 2, then you can turn it off by using
echo 0 > /sys/class/leds/led1/brightness # Power LED
It is taken from the last answer from post I referred.