I can still remember going flying with my dad around PHX when the strike was ongoing. All the civil airports with towers, with the exception of KPHX in the Phoenix valley, all were uncontrolled fields now since their towers were unmanned. KPHX tower and RAPCON had USAF ATC controllers from Luke and Williams AFBs manning it, the airspace being only a TRSA at that time. There was a "reservation system" for GA in order to file IFR.
In fact, there was an accident at KFLG of a landing collision between a SKW Metroliner departing in IFR conditions while a MU-2 was landing, destroying both planes but with no one perishing. A tertiary factor was the lack of ATC services due to the tower being closed for the strike.