Congress authorized the Prez to take the Army to Iraq to use force to kick ass and take names.

Or to put it a different way, they wimped out.

It's their job to declare war, but instead they gave the Prez a blank check letting him take the country to war if he choose too. Well... he choose to.

And yes, we didn't get UN permission.

I don't know if this makes the military action "illegal" from an international perspective. The US is the world's cop, so maybe, maybe not, or maybe our being on the Security Council means it's a moot issue. But inside the US the Prez did get permission from Congress to do what he's done, so that part at least seems legal.