First of all, it is important to distinguish Individuals and States. States themselves cannot be charged for war crimes, individuals are (i.e: soldiers). The war against Iraq wasn't declared illegal because it's aggressive and because their are war crimes. It's the concept of self-defense that was into play (I'll explain later).
The only international court that could charge the STATE is the International Court of Justice. Let's say Iraq wants to bring the US to the ICJ, both states have to appear to court, otherwise the judgment won't be binding, and the Security Council will take a decision. As you know, the US is one of the 5 permanent members of the security council and has a veto right, thus they won't let the rest of the SC impose a decision on them. Moreover, it would be very miscalculated for other states in the SC to offend the US.
Then you'll probably ask what the Permanent International Criminal Court could do about that. That court only comes into play when there are war crimes. It judges individuals, not states. (and the US did not even ratify the Rome Treaty, which is the founding base of the PICC). In addition, the state in which the crime has happened will always have "priority" in judging the criminal. There's a PICC trial only when the state cannot or is not willing to judge the individual.
As I was saying, the war against Iraq was declared illegal because, according to the UN, any war has to be related to self-defense, and according to the UN's definition of self-defense, it is not, in that case. That's why the US are trying to change the definition of self-defense. According to them, a state shouldn't have to wait until it's attacked to have the right of self-defense. So the UN added a new Article (Article 51) you should find it easily on the UN's website. But it doesn't make the US happier because the state that wants to "self-defend" who have to reveal its plans before it actually invades the other country.
If you are interested in knowing more about the UN, let me know, I can send you more information! I'm not a specialist of American politics, but I can answer questions about International law and the UN.