/u/restricteddata has an answer to the question here.

Of course, more answers are always welcome.

Hello!

(sneaky edit: this comment responded to another that has since been removed. That's why it's partly structured as a rebuttal/some of the context points are around very specific small issues, and why it talks about another contribution.)

This is a three-part answer. First, I clarify and refute some of the points made about international law in another answer. This is important because those inaccuracies effect our framing of the situation, including as concerns the content of the law. Second, I give a very different interpretation of the actions of post-war presidents up to and including the year 1990 to that given by another contributor. Lastly, is a somewhat meta point: a plea for accuracy when discussing the law. International law is messy, and 90% of answers (including, inevitably, this one), miss important points, but there's a responsibility on people who study it or work in that field to effectively communicate.

Please forgive that the first part of this is theory, not history – you need it for the history to make sense!

As a starting point, this is really a question about international criminal law (ICL) as opposed to international humanitarian law (IHL). IHL rules lead to State responsibility; ICL rules lead to individual criminal responsibility. One of the hard parts of this question is that in some ways, because of the customary status of the Nuremberg principles + their incorporation into other documents, it almost asks for legal advice on whether you could successfully prosecute a sitting head of State in a modern court. In the interests of not getting into a politically heated discussion about, e.g., the ICC, I answer the core of your question on the assumption that hypothetically, you could conclude a prosecution based on the Nuremberg principles alone. This wouldn't actually work, but it answers the question you're asking.

Background: the content of international law

International law is a system that governs relations between different international actors. It primarily creates obligations for States, but certain international organisations can agree to bear obligations, or enjoy protections under the law. Some organisations, like the ICRC, enjoy a unique status under international law, but only because States have imparted that upon them.

The basic assumption underlying international law is drawn from the Lotus case, and often read as “whatever is not prohibited is allowed”. A better reading, though, is “a rule does not exist without implicit or explicit agreement”, and that restrictions should not be assumed upon the rights of States. Where there is no rule, there is also no opposability, which means there’s no ability to make a legal claim. This is important: it’s not “States can do what they want”, it’s “restrictions exist only where they are agreed”.

International law, as far as States and day-to-day practice are concerned, only comes from treaty and custom, along with certain general principles accepted by all nations. It does not come from judicial decisions or the writings of publicists; those are subsidiary sources for confirming the content of the law. The writings of “the most esteemed publicists” is taken today to refer generally to international lawyers. These sources and subsidiary means are included in the ICJ Statute, which was originally the PCIJ statute after World War One. This doesn’t strictly mean that these are the only places we can find law, but it does mean that as far as the ICJ is concerned, there is no other source besides treaty, custom or the application of a general principle.

Treaties are any written agreement between two states, and a customary law is one backed by widespread state practice and opinio juris. Time is relevant, but not necessarily vital, for custom. Ultimately, finding it is a subjective process. Persistent objection by a State, from before a rule comes into existence, can mean that it is not bound by that rule. This was the case in Fisheries (UK v Norway) [1951].

International law is prone to fragmentation. One good example of this is that the ICTY applied a different test to the ICJ to identify control over armed groups for state responsibility purposes. There are ways to get around fragmentation through interpretation:

• Specific rules override general ones. This is why, during war, it can be legal for a state to kill people. This is called lex specialis and can also result in the creation of self-contained regimes.
• A treaty overrides conflicting customary rules between its parties, unless a customary rule is also jus cogens/peremptory.
• Generally, we try to read law in a harmonizing way, i.e. that a State’s presumed intention is to be consistent with its other international obligations.
• Sometimes, if rules can’t be consistently interpreted, a newer rule will override an old one. This is called lex posterior. It’s not always true, and it requires knowing the will of the parties involved.
• Sometimes, a rule might be invalidated for conflicting with a jus cogens rule, an obligation erga omnes, or article 103 of the UN Charter (which gives it primacy over other treaties). Every jus cogens norm is erga omnes, but not every erga omnes rule is jus cogens. The difference is that a jus cogens/peremptory norm is one from which no derogation is permitted, and an obligation erga omnes is owed to all states. This generally applies to treaties.
• The Vienna Convention on the law of treaties allows for taking “any relevant rules of international law applicable in the relations between the parties” into account when interpreting a treaty. This is the idea of systemic integration, where we interpret treaties in their broader context to try construct a coherent whole.
• Consistent interpretation: this is more for domestic courts, and means interpreting the law domestically to give effect to international obligations.

The other answer pretty accurately describes responses to violations of international law:

• Public statements that the law has been broken and attributing responsibility;
• Retorsions, e.g. the use of unilateral sanctions (although even this is arguably a countermeasure) – lawful, but unfriendly, actions;
• Countermeasures/reprisals – reciprocal violations to return to compliance with the law;
• Litigation for internationally wrongful acts.

However, the use of force is not a lawful action under international law today, except in self-defence or with the consent of the Security Council. This has been the case since the 1928 Kellogg-Briand pact for most nations, and now is explicitly included in article 2(4) of the UN Charter.

The status of the Nuremberg principles

The Nuremberg Principles and the Nuremberg Charter are different things. The Principles are a document of the International Law Commission. The Charter is a treaty establishing a sui generis international military tribunal. For our purposes, this means the issue of whether a State was party to the Charter is irrelevant, but, for clarity, the Allied powers were all parties – the ICRC page lists subsequent ratifications. You’ll notice that also missing are the UK, France and Russia – aka, the States with the most responsibility for the Nuremberg Tribunal. This is clearly reflected in the text of the Charter itself as well. From a legal and political standpoint, the Allied powers refusing to endorse their own criminal tribunal would have been counterproductive at best.

But anyway, the principles showed that the Nuremberg Charter’s content may have constituted principles of international law, following UN General Assembly in Resolutions 95 (I) and 177 (II), which affirmed the principles contained within the Nuremberg Charter and requested the ILC formulate them in writing. While a UN resolution does not ordinarily create law, it can be an important expression of opinio juris – the belief that a State is bound. That's the right way to see the resolutions and the ILC principles - as expressions of a belief that the law existed and was binding, but required clarity as to its content. The principles carry on, in one form or another, in the statutes of every international criminal tribunal today. They are now customary international law and some have been incorporated into other treaties, including in the human rights sphere.

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