Installed Self-Grounding 3 prong in place of 2 prong
So you have metal boxes? The findings of 120 V hot to ground, 120 V hot to neutral, and low resistance neutral to ground are consistent with separate ground and neutral paths to the panel and that is almost certainly what you have.

The ground and neutral are supposed to be connected in the panel and only in the panel. If that is what you have, the resistance you measure between neutral and ground at a receptacle is the lengths of neutral and ground wire back to the panel where they are connected.

EDIT

You need to determine that there is a separate ground path (metal conduit or a ground wire) all the way to the panel. The other possibility consistent (I think) with your measurement results is that someone has connected the grounds of the each receptacle to the neutral in each box. I think this is called a "bootleg ground" and it is not according to code and not safe. I think you would see evidence of this inside the boxes.

Time for you to take pictures of the inside of one or more boxes and attach the picture to your question. Also time for one of the experts to comment.

EDIT2

Bootleg ground wiki. You could take off one or more faceplates on receptacles. You could take off the "dead front" on your panel and see if you have ground wires there. Of course, you could be grounded via conduit.