I have a 24 year old 90+ furnace (Nordyne) that will not complete it's heating cycle. If I turn off the power switch and then turn it back on, the furnace will ignite and run until temp is achieved. The furnace will then shut off the gas and blower, however the exhaust fan will not shut off to complete the heating cycle. In order to restart the furnace I must manually shut off the power switch and turn it back on. I have already changed the igniter module but this did not fix the problem. Could I have a vacuum problem?

Sounds like you have a faulty draft inducer relay switch. If the draft inducer doesn't shut off after the call for heat has ended, that means the draft inducer is still getting power which is supplied from the either the control board, or in your case a relay separate from the ignition module.

I believe what you are looking for will be called a "induced draft relay"

If you can post some clear pics of the inside controls on your furnace, along with the wiring diagram I should be able to tell you which part needs to be replaced before you spend any more money on parts that don't need to be replaced.