I do not think the engine can be running richer with the oxygen sensor connected then with it disconnected. When you disconnect the sensor a 0 volt signal is sent back to the ecu which richens up the fuel mixture. The same thing happens when the oxygen sensor goes bad and you notice an drop in fuel mileage.

You may have vacuum leaks that admit excess oxygen and make the engine run a leaner fuel mixture. When you unplug the oxygen sensor the mixture is richened up and the engine smooths out. Try checking for vacuum leaks by spraying water, WD40 or Carb. cleaner(caution, they're flammable), etc., around the injectors, intake manifold gasket, basically any place on the intake manifold that there is a gasket or o-ring. If the engine speed changes when you spray a component then the seal is bad and should be replaced. Check that the rubber boot between the fuel distributor/mass airflow sensor and the throttle body is in good shape and clamped tightly. Replace any hard and cracked vacuum hoses. After 22 years in operation, the fuel injectors may not have an optimal spray pattern and/or even deliver the same amount of fuel to each cylinder which would make it impossible to set the fuel mixture correctly. Are all of the sparkplugs the same tan color indicating even firing?

Check the basics first(plugs, wires, distributor cap/rotor, etc.). Let us know what you find.