Wall Outlets Don't Work?

My parents moved into an older home and the outlets in an extra bedroom all worked until a month ago. Using a multimeter, I am not able to get a reading on any of the outlets. (Using an non contact probe, I got a hot read on the outlets). The only reading that I get is when I place one of probes in the hot and one in the ground. The light in the room is working fine and is on the same circuit. I replaced all of the outlets this afternoon, but it didn't work.

I did notice that the neutral wires were attached opposite of the hot wires, but I am not sure if that matters. Another thing that I noticed was at the panel. On the neutral bar, in a few places, there is more than 1 neutral wire in a few of the slots. I am not sure what I should do next, other than have them call in an electrician.

By Phillip C.