Strange indeed.

Do you have any communication/microwave towers nearby? Power lines?

What doesn't make sense is the objects are in contact with ground, and so are you, so where does the "step and touch potential" (i.e. the voltage differential you experience) come from? (In addition to where does the current come from?)

[That is, we are all "birds on a wire". That is, it's all relative. There needs to be a DIFFERENCE in voltage to get a current to flow. Example, if my yard was at 200 volts compared to my neighbors yard, I wouldn't get shocks, because I and everything I touch is at 200 volts (compared to someplace else), but at zero volts compared to me. Understand? ]

Similarly if you ground a meter then measure ("grounded") tiles, how can there be a voltage? Either the tiles or the "ground" reference your using is not at zero volts.

In this case, how do you "ground" the meter?

At first I would say, you have voltage/current on your panel ground conductor (i.e. an floating/ungrounded electrode system) that you are measuring/feeling when you touch part of this system (the AC system / piping) and the "real" ground at the same time, but this doesn't explain the root ball where I assume you are away from the house?