Hi Joe, I remember well my first run-in with this seemingly unusual setup. What you have is indeed a 24v. relay system that was briefly marketed, primarily by GE, which never took off.
From my experience with the system, I found it impossible at the time to find replacement parts, let alone find anyone who didn't first think I was looney when explaining what I wanted parts for. But, that was about 12 years ago, so with computers more common today you may not be called crazy, but the availability of parts will likely be a problem until you find the right source.
In looking this subject up, I did find the following thread of posts which gave some better information; I hope it will do you some good. Best of luck!