but if the order is A0, A1, A2, A3 is read, it absolutely makes sense.
One possibility is that the microcontroller is damaged - has this been ruled out?
Tried it on an Uno and a Mega... Same exact problem on each.
Your observations do not tally with your description of the circuit. So the circuit is not as we understand it from your description.One of the first things I suggest you do is measure your pots with a multimeter and make sure they really are 10K from end to end.