1 zone of my 2 is not working. Even if I shut the heat to "off" the baseboards continue to feel extremely hot and the temp in that zone is almost 90 degrees. Called the oil company for repair and the guy basically said that nothing could be done. Prior to today I had no problem and now it's a sauna up there. PLEASE HELP as I have my newborn twins sleeping in this zone.

Called the oil company for repair and the guy basically said that nothing could be done

I would be calling another service company since in this situation there is not much you can do unless you know how to work on the zoning controls and all there associated parts and pieces.

The possibilities are

Defective thermostat
Defective thermostat wiring (damaged)
Defective zone valve
Defective pump controller (contacts welded)

You will need a electric meter and know how to use it. (To test the parts and find the problem)
You will need the appropriate hand tools to disassemble and replace parts.
You may need a torch if it is necessary to replace the entire zone valve.

This is for starters. I am sorry but I have no magic cure for this type of problem since zone systems are a bit more complex to diagnose.

About the only thing you can check and do is to make sure the thermostat is turned off or down all the way so it is not calling for heat.

If you have the Honeywell brand zone valves there is a lever on the end that can be opened manually. Make sure it is set to the automatic. Lift and release if necessary on the lever. If the valve is stuck it might close.

See page 12 figure 10. Look for manual and auto lever on valve. Make sure it is in the automatic mode.

http://customer.honeywell.com/techli...0s/60-2133.pdf

Oil-fired... is this system forced air, hot water, or steam? Based on your description of the problem, I'm guessing water or steam. Sounds like a zone valve is stuck or the motor has failed, so it won't close and is keeping the boiler under demand. If you can locate the valve, you may be able to rotate it to the closed position manually (depending on type), but ultimately you should call in a pro. If the system is forced air, then throw out everything I just said... and call in a pro.