There is no Global body that makes laws!
There is no international legislature (the UN ain't it), there is no international monarch. They are the two groups that make laws. When there is a 1:1 correlation between cause & effect, if you don't have the cause (international legislature) you can't have the effect (international law).
So despite the lies that a bandied about, international law doesn't exist.
What people often mean when they say "international law" is "treaties," but they usually have some agenda they are hiding behind and intentionally misleading you. I assume that since God is dead and humans can no longer appeal to the moral authority of God that they feel the need to appeal the moral authority of some other fictitious being. In this case, international law (aka global standards).
Now on to treaties.
Treaties are just agreements between governments to enact laws. They aren't law by themselves. The US Constitution gives the President the authority to make treaties, but Congress gets to ratify and then make laws based upon them.
So, the US & AU make a treaty to do W, X & Y
When it gets run through the AU Parliament they don't like W. So they pass a law that allows for V, X & Y. That law is only enforceable in AU. It is an imperfect implementation of the treaty, but an implementation nonetheless. It is like a standard that is implemented but not fully.
Same thing happens in the US Congress. But they pass law with X, Y & Z.
Now you have 2 national laws. A AU law. A US law. You don't have an international law. Why? No international legislature remember.
You can sue in AU under the AU law, but not the US law. So in AU you are entitled to V, X & Y.
You can sue in US under the US law, but not the AU law. So in US you are entitled to Z, X & Y.
No where can you sue under the treaty. You never are entitled to W. Because te treaty (which entitled you to W) isn't a law, just an agreement to make a law.
You can't sue in NZ under either the AU or US laws. Because NZ, has neither of these laws and their courts don't care about US or AU laws.
Now we mis-use the term "treaty" to refer to both the AU & US laws collectively, but neither of them is really the treaty as negotiated by the PM/President.
Hey what about these international courts?
Well, they are really arbitration bodies.
They have no legal power beyond what the individual nations give them.
The UK may pass a law giving ICC judgments full effect, but that is due to the UK ceding sovereignty to the ICC, not because the ICC is inherently morally superior or because of some international law (which doesn't exist remember).
Now the US doesn't agree to cede its sovereignty to the ICC. So the ICC has no effect in the US.
Why no power beyond what the individual nations give them?
It comes down to a concept called jurisdiction.
See, ultimately might does make right. Not moral correctness, but the right to do something is ultimately based upon your ability to enforce that right.
To enforce a court order to, for example, the ability to forcibly imprison someone, take their personal and real property from them, you need an army and a police system. Nations have these things. NGO bodies don't. Even the UN has no standing military. It relies on borrowing the military of its member nations.
If the ICC has a judgement it wants enforced in the UK, it needs to get the approval of the UK government to use the UK police force to do that. Alone, the ICC is impotent.
Ultimately, every country acts unilaterally. Every country implements their own version of treaties. Every country decides whether or not to cede sovereignty to an international arbitration board.
When you start with the faulty assumption that there is a black and white "Law" you can appeal to, you get incorrect and faulty conclusions. What you get is some fiction that can be molded and bent in order to fulfill the speaker's political addenda. The entire premise of "International Law" is intellectually dishonest. The term is designed to mislead and cloud logical thinking.
The phrase "International Law" should be regarded by lawyers with the same disdain historians/archeologists reserve for "The Chariots of the Gods" or psychologists have for phrenology, the idea that you can tell if someone is a criminal by examining bumps on their skull.