I have orange gunk that clogs up my water lines. I can take off all the shower heads and open up all of my water lines and get them all cleared out and running clear, but as soon as there is no water running in the house all of my lines get clogged again. I had a plumber come out and he told me the pipes were good. He replaced all of the supply lines and flushed out the system, but the problem is back. I just noticed that the water softener that I was told was disconnected, may not be disconnected. Could this be the problem?

If your water softener is defective, and not bypassed, it could very well be the culprit. Sounds like you are getting media from the softener. I would start by putting the softener on bypass, or completely removing the softener from the system. Reflush all lines, and see if the problem is taken care of.