Oxygen sensor ?
 

What does an oxygen sensor do? On an 88' 190E is it easy to replace? Where does it go?

It senses how much oxygen is in the exhaust. This tells the car if the engine is running rich or lean and then adjusts the air/fuel mixture accordingly.

I don't know exactly where yours is located but it should be somewhere in or near the exhaust manifold, look around near the catalytic converter too.

They are typically easy to replace, I've done it a few times on Ford's.

It is a cylindrical shape that is maybe a half inch in diameter and about 3 or 4 inches long.

Is your gas mileage really bad?

It can fail in several ways....

overriching... = bad mpg.
overleaning... = stalling.