do you need a oxygen sensor when you remove emissions from 84 monte carlo?

Answer 1

Removing the emission control system from a car with computer control is a waste of time. The car will run poorly and get less mileage. There is no advantage unless you are going to replace the camshaft, heads, intake manifolds, exhaust manifolds, fuel injection system, distributor, etc. Then you would have a race car.
The O2 sensor manages fuel/air ratio. Unless you did the above changes then you will end up with a poorly running car.

Answer 2

If you're pulling everything off, you don't need the O2 sensor, but you will need something to plug the hole that the Os sensor is in. An O2 sensor works great for plugging that hole. Just unplug it.
Why are you yanking all of the smog equipment off?

Since this car uses a feedback carb, you can change the intake manifold and carb and the engine will run fine. It won't pass any smog inspection though.