An A319 flight crew encountered numerous anomalies and ECAM messages when undetermined gremlins infiltrated the aircraft's electrical system. They safely diverted to a nearby airport. Their difficulties were enhanced by the inability to communicate with Dispatch or Maintenance on a timely basis.

Narrative

Shortly after level off at cruise both the First Officer's screens and the lower center screen had a line through them. We had an ECAM for DMC2 failure. The ECAM went away and the screens came back to normal; however; the fuel used showed XX. The ECAM DMC2 continued to cycle on and off. We read the recent company bulletin regarding electrical anomalies and referenced the FM (Flight Manual) for DMC2. The next ECAM was STBY PITOT. We referenced the FM. Other than the DMC2 and STBY PITOT on the status page; other items seemed normal. The flight attendants had no abnormal signs in the back.A short time later the auto pilot and auto thrust disconnected and the FD went away. We were not able to recover any of these items. We advised ATC that we were no longer RVSM equipped and we were given a descent. The First Officer was flying and I was trying to get Dispatch on the radio. I tried the 'call me' function and got a 'button not active' message. I typed a message to Dispatch and received three different frequencies and was not able to establish voice communications on them.During this time we had a L/G SHOCK ABSORBER FAULT; over speed warnings (we were not over speeding but were above 280 KIAS) and ENG THRUST LOCKED at least twice (auto thrust was supposedly off and throttles were being used manually). We started the APU and used it to power the AC2 bus and un-powered the #2 generator.Through ACARS messages with Dispatch we elected to divert to a nearby airport and notified Dispatch of such. We talked to the flight attendants and had them do a cabin advisory. I made an announcement to the passengers to tell them what was going on. At this point I did not know what was going to happen when the gear came down and we tried to configure for landing. Just prior to an early configuration for the approach I tried to reconnect the auto pilot and auto thrust and they appeared to be working correctly. I used them to transition onto the approach but flew the approach by hand. We landed uneventfully and taxied to the gate. Later; the A Flight Attendant said that the video screens had extended and retracted on their own during descent and that the oxygen masks at 2EF had deployed on their own. Aside from the obvious airplane issues; the item that significantly increased our work load was the inability to communicate with Dispatch or Maintenance Control in a timely clear manner.