Celica radio vs. ABS computer

Who has some ideas before I REALLY dig in on my kid's car.

1995 Celica in good condition with low-average miles. Recently the ABS
check light started coming on, seemingly at random, with a variety of
codes such as:
Right Front wheel speed.
Right Front sensor damaged.
Right Rear wheel speed.
Stop Light Circuit.
Pulled the right front wheel and checked cabling. Visually OK.
The other day the ABS light went OUT for a while and the brakes went
into ABS mode during normal, conservative driving.

This seems to happen only when the radio is on. It has a sub-wolfer
that was professionally installed a year ago.

First, you need to verify that the wheel speed sensors on the corners
indicated by the codes you had present are functioning normally. This
includes, checking for chaffed wires, inspecting the sensor head for
debris, checking the sensor rotor for damage or debris, and if possible
make sure that you are getting a nice AC waveform from the sensor
connector when the wheel is spun. The codes you mentioned aren't as
shotgun as you think, they all seem to be pointing toward the fact that
the speed sensors aren't able to get a consistent signal.
The reason the ABS system engaged while you were driving is because the
computer perceived different wheel speeds while braking and activated the
system. Another cause of this on earlier systems is different sized tires
due to wear. This can cause a difference in wheel speed and confuse the
ABS computer.
As far as the radio, check the basics first before you go hunting some
bizarre correlation between these two unrelated systems.