Once the Zentraedi have annihilated your military bases and airfields, it's already too late to try any significant resistance with mechanized forces. Variable fighters must be unbelievably complicated, full of unnecessary moving parts that will break (especially under combat conditions) and will eventually require the aircraft to be stripped down and overhauled. It is not a question of if they break down beyond the capabilities of simple field repairs, it is when. Things break, and the more complex they are, the harder they are to fix when they are seriously broken. VFs are absurdly complex. Every single moving part on it is a potential failure. Compared to working on a VF, working on a normal aircraft would be trivial.
Without established military bases and a decent logistical train, your only option is insurgent tactics with (human) infantry wielding small arms and simple devices like small rockets and mines. Essentially you'll be operating at the level of Palestinian or Iraqi militia. Variable fighters are completely useless to such a force; you cannot maintain such costly, complicated, and sophisticated machines. They eventually will get major failures that require overhaul, you will run out of spare parts, you will not have the ability to build more. If the UN government wanted to fight off an invasion of Zentraedi infantry after the sudden and nearly total loss of their military facilities, the obvious choice would be to build man-portable anti-armor weaponry and light artillery like mortars and rockets, and in vast quantities. A thousand men with futuristic AT4s will do far more good than a squadron of variable fighters, they'll be far more mobility and stealth than variable fighters or Zentraedi and be able to use cover that they cannot, and they will cost less and be more feasible to maintain in desperate circumstances.
The variable fighter is a disastrous idea for either conventional or asymmetric warfare. Normal planes and tanks are far more useful for a direct confrontation, and shoulder-fired infantry weapons capable of taking out Zentraedi foot soldiers or Regults are far more useful for a guerrilla campaign. Using overtechnology to built fold-capable, fast warships to get enough people for a self-sustaining diaspora somewhere else fast might be a decent option as well, but of course there is the risk of being tracked or slaughtered before the project is completed.