Circuit Not on Any Breaker, but Off with Main Breaker
It's not necessarily the cause of your problem, but I saw a situation just like it once:


Plug a light into the socket and see that it is "on".
One by one, turn off and on each breaker in the panel.
Go through the entire set of breakers, and the light never goes off.


Eventually discovered cause:  one circuit had been wired in a loop, with a separate breaker at each end (fortunately on the same side of the line).  Cutting off power at either end had no effect on the light; both breakers had to be turned off to shut off the power to the circuit.  (This also meant that each outlet on the circuit was providing twice the normally allowed current.)

If this is what you have, try this to find the two breakers:


Plug in the light.
One by one, turn off (but not back on) each breaker in the panel.
If the light never goes off, this isn't your problem.
When the light goes off, mark that breaker as special.
One by one, turn on the breakers that you had turned off.
When the light appears again, mark that breaker as special.


Turn everything back on again, and confirm that the light goes off only when both of the marked breakers are off.



If you are sure that this really is the cause of your problem, arbitrarily choose somewhere in the circuit that has two adjacent outlets (both should behave the same way with respect to the two breakers).

Both outlets should have a pair of wires coming in and a pair of wires going out.  Determine which pair of wires goes between the two outlets, and disconnect it at each end.

Verify that one outlet is now controlled by one breaker, and the other by the other.

Make sure that when both breakers are on, no other outlet or light is without power.

Verify that the disconnected wire has no power when all the breakers are on (I'm assuming you know how to work safely with electricity and won't be testing it with your tongue.)

If you can, remove the redundant wire.  More likely though, you will have to cut it short, and/or put marrette caps on the end of each wire.



Alternatively, rather than breaking the loop back into two separate circuits, you could disconnect the line from one of the circuit breakers, and remove or cap that line (attach a note to it saying it is the end of whichever the other breaker is).