I have recently noticed that when my car is warm, at gradual take offs after stopping, I hear a clicking or knocking noise. I checked for loose bolts or debris. Nothing. I took it in for service and was told that the oxygen sensor needed to be replaced. I got that done and still experienced the same noise. This noise only happens when I accelerate after stopping, mainly at the beginning of accelerationg from 0-20mph. Any thoughts or suggestions?

does the knocking noise happen on corners or in a straight line? Around corners I would check your cv shafts they can also make noise in a straight line take off if they are really bad.

It happens on straight lines and curves. Anytime I begin to accelerate up to 20 mph. Over 20 mph, I don't hear anything.

There is not as much tourqe on the half shafts when you are up to speed. look behind the tires and look at the rubber boots on the axle shafts to see if they are ripped open if so replace the axle or axle shafts because they are junk

The boots are still in one piece. No leakage or irregularity around the boots.

I would still say it is the boots. this happened to me and everthing you describe happened to me. New driveaxles cost me 60 bux for the long side at advance auto parts. Take it down to your mech...mine just threw my car up onto the lift and took him 2 seconds to confirm w/ me that it was the boots....i had pretty much new it was already, i just wanted to make sure which side it was....AND DON"T JUST REPLACE THE BOOT....REPLACE THE WHOLE DRIVE AXLE...its cheaper and easier