A story setting in which aliens invade planet Earth much as the United States invaded Iraq or Afghanistan is hardly ironic in and of itself. What I mean by "as the US invaded" is in using the same sort of method--aliens hitting us with technology and precise strikes so advanced we can't counter them, specifically targeting people from far enough away (say high Earth orbit) that there's nothing we can do about it before they destroy our capacity to resist. The aliens would also be the same in trying to avoid hurting the general populace, eliminating our leaders, and establishing new leaders under new rules. Alien troops could work side by side with human troops for the purposed of training them to "take over" while they simultaneously work to rebuild our shattered industries along their lines. Alien forces would continue to fight a human counterinsurgency, as humanity as whole adopts Afghan and Iraqi style tactics of suicide bombings and intimidation.
This sort of setting would be perfect for a story intended as an anti-Afghan or anti-Iraq War commentary. As in, "Of course insurgents use brutal methods, but we would too if we were forced to do so by superior alien technology." Empathizing with the insurgents is such a natural offshoot of this setting and using science fiction as social commentary on current events is so common, I wouldn't be surprised if there aren't already half a dozen or more tales that are in effect variations on this type of story. So obvious is this, that while it might have the potential to be interesting, it's hardly original and certainly not ironic.
But if you take the setting and make it so the aliens really do have what even honest humans recognize as a good justification for overthrowing our government and taking over, then you have more potential for irony and originality. You can make the justification whatever you wish, which naturally would shoot out from social commentary. The aliens could think our leaders are destroying the planet, for example, necessitating their takeover to save it. Or they could be horrified we allow abortion or fail to vigorously attack the human slave trade or let people starve to death or keep animals as pets or have economic systems specifically geared to benefit an elite minority. Whatever political issue an author could wish to harp on would be used as a justification, either left-wing, right-wing, or from somewhere in the middle.
Of course, it would be more original and more interesting for story purposes to come up with something that is not a current political hot button issue. An example a bit off the wall would have the aliens outraged that we don't allow children to vote or hold political office. Their political new system would systematically work to empower children and outright give them the vote. Perhaps less off the wall idea would be they object to us passing laws that have not been screened by scientific methods and computer modeling to ensure the laws actually accomplish what they are supposed to accomplish. How barbaric of us! How much suffering our foolishness causes!
Correctly done, the alien way of doing things, their reason for having taken over Earth, should be shown as having real merit of some kind, no matter how strange it may seem. Insurgents would of course fight the aliens nonetheless because they are on our world and don't belong here. Actually, they would probably also mock the alien reasons, even if most people saw that they worked. That way, both the alien overlords and the human insurgents could be shown as sympathetic characters overall, with individual villains existing among both groups.
That's the way I'd recommend writing an alien counterinsurgency story.