But first I guess, they technically need to impeach Bush and Cheney...then they can go after them as the common criminals they appear to be.
As to complying with the World Court, it seems that there is a law morally compelling Congress to cooperate with regards to the Bushco trials:
No lawyer is going to take that passage to mean the United States cedes sovereignty to a World Court.
It says they have the power to, not that they must. But in order to protect the US citizenry en masse, from backlash of atrocities committed unjustly to other nations by the harbored-fugitives Bushco, Congress is really mandated to prosecute them, because Congress is in charge of maintaining protective services for the citizenry of the US.
The Executive is charged with the defense of the nation according to interpretations. The Executive will simply argue that the role as Commander in Chief supercedes the role of Congress.
Further, in terms of the Constitution, Congress has no power to "prosecute" anyone. That is the Judiciary's job.
Laws like these are somewhat broad and open to interpretation. It could be interpreted that Congress might choose to repel invasions (could be interpreted as "random acts of terrorism against the citizenry" ) by holding it's nefarious officers or former officers of state to prosecution for acts deemed to agitate compelling and well-founded worldwide hostilities towards the citizenry. So if the Hague finds Bushco blatantly guilty of acts of unforgivable and illegal atrocities within the World Court, Congress may then act on behalf of securing the safety of its citizenry from predictable backlashes by cooperating with extradition and sentencing of the criminal element responsible.
In fact, I would think it would be mandated?
No. The Hague can say whatever it wants, Congress will ignore it. Further, under US law, acts of Congress or Executive Orders supercede international law. Therefore, you can say Bush broke some international law, but if he did, it was done with an Executive Order or an act of Congress which automatically nullifies any international law. Therefore, the Hague has no case.
Therefore, you can only perhaps try him under domestic law if you can come up with a case. Since the OLC and Congress have pretty much backed up every action that was taken, there is no case to be had.