Sorry for the slow response, but when in the process of taking out the breakers to investigate the bus bar I figured out what was going on and it took me a few days to confirm it. The two bad breakers were in the same row of my sub panel, and it dawned on me that if one the lines from the main panel that feeds sub panel was bad, that could be causing my problem. So I tested the two breakers (tandem) in the main panel that were feeding my sub and sure enough one of them was putting out 25V. So I replaced the tandem breaker in the main panel and now everything is working agin.
Thank for your suggestion about the breakers being in the same row, which got me thinking about the problem in a different way.
What you are describing is called a Multi-wire Branch Circuit, and it is completely legal (given that it's done properly).
The first problem, is that it doesn't should like the breakers feeding this circuit are handle tied together. It should be feed by a double pole breaker, or the two breakers handles should be tied together. You should not be able to shut off only half the circuit (red only or black only).
As for the voltage. I'd suspect it's phantom voltage (inductive coupling), and so should not cause any problems (especially if the breakers were properly tied together).
If the breaker for the "red" conductor is off, and current is flowing on the "black" conductor. Because the conductors are parallel, and in close proximity, a voltage may be induced on the "red" wire. There should be no current, however. So if a load was introduced, the voltage would drop to 0.
You can determine if it really is phantom voltage, simply by using a low impedance voltmeter. The low impedance meter will read 0 volts, while a high impedance meter will read the phantom voltage. An analog meter is one example of a low impedance meter, though some digital multimeters are able to operate in both modes.
Best Answer
Looks like a feeder fuse(s) opened, measure a-b a-c and b-c , some of the measurements show voltages as they are feeding through other devices. If you measure low voltages at your main panel call your power company and tell them you have lost phases. This happens all the time in industrial sites where a fused feeder gets over loaded sometimes a short on 1 phase takes out a 2nd then the circuit breaker trips, you still have power on 1 leg so there is no breaker probably fuses at the pole.