Water Heater PRV keeps opening
20 years old, it's almost certainly time for a new one unless it's of very unusual construction - like stainless steel.

If water:


  overflows from the top of the pipe onto the floor


Then the overflow pipe is not correctly routed - it should go DIRECTLY down to the floor. I can see it going sideways in the picture on your other question. It also appears to be reduced in size, which is a code violation, and if it's positioned so that water is held (trapped) in it, that's a code violation.



Many hot water heaters need an expansion tank to avoid over-pressurizing the PRV when heating a slug of cold water when no water is being used. Most PRVs are rather bad about resealing when they have been "exercised" a bit. Both of these may play into your problem.