If multiple hostile figures and friendly figures suffer damage/strain simultaneously; in what order is the damage/strain resolved, or who chooses the order? For example, let's say Captain Terro uses Flamethrower and it hits both hostile and friendly figures; which figures (hostile or friendly) would resolve their strain first?

All strain/damage is applied simultaneously from these abilities. If suffering causes other abilities to trigger, then the best guess is that the controller of the figure with the ability that caused the suffering chooses which figure's suffering is resolved first. If multiple abilities trigger simultaneously for a single target figure then it comes to the timing conflict resolution order of individual abilities.

However, in skirmish all suffering of strain triggers the possibility to discard a card to cancel the damage from suffering strain.

I would say Terro's controller decides, but I don't know of a definite ruling about it.

(There's a potential fallback to "the activating figure decides the order" when timing conflict resolution doesn't give an answer.)