I am still working on it.
I checked it out visually after the early round of suggestions, but could not determine myself the nature of the problem. I need to have it checked out by a pro, but I am thinking that it is a problem of the driveshaft center support and bearing or Jsmith's earlier suggestion of differential mounts. It looked to me like differential mounts would most likely be the problem, as they plugs look very old and worn out. But when I tried to move the differential up and down, I couldn't budge it. I will also try out Jsmith's latest suggestion, and appreciate all the comments very much. My noise is not really a "clunking" type of noise, but more like a hard tapping noise. It also comes and goes, and sounds exactly like the problem of Speedrxer. I am going to see my independent about this very shortly. Thanks.