Article 2(4) of the U.N. Charter says "All members shall refrain in their international relations from the threat or use of force against the territorial integrity or political independence of any State" but is that enforceable?
Yes, ultimately by states taking action under Article 51 of the Charter, if all else fails.
EDIT: But, while the Security Council veto Russia wields can block the main UN enforcement mechanism, there has been a General Assembly fallback since 1950 via the “Uniting for Peace” process; while the UNGA has acted using this process already in the crisis without explicitly calling for enforcement action, there is nothing preventing it from revisiting it with stronger terms.
With respect to the UN charter, it's enforceable in the sense that any international regulation is: if you care enough you can get your guns and shoot the other guy if he doesn't follow the regulation. But otherwise, no.
The comment I was responding to was claiming they were breaking international law and my hope was that there is an avenue to enforce that in the long term.
The lawyers answer is relevant here: It depends.
Is the illegal attacker the US or a major NATO partner? Nothing much happens.
Is it an attack between third-world-countries? Noone really cares.
Is the attacker a major opponent of "the West"? Well, we're seeing this play out right now.
Chapter VII: Action with Respect to Threats to the Peace, Breaches of the Peace, and Acts of Aggression
Article 39
The Security Council shall determine the existence of any threat to the peace, breach of the peace, or act of aggression and shall make recommendations, or decide what measures shall be taken in accordance with Articles 41 and 42, to maintain or restore international peace and security.
Article 40
In order to prevent an aggravation of the situation, the Security Council may, before making the recommendations or deciding upon the measures provided for in Article 39, call upon the parties concerned to comply with such provisional measures as it deems necessary or desirable. Such provisional measures shall be without prejudice to the rights, claims, or position of the parties concerned. The Security Council shall duly take account of failure to comply with such provisional measures.
Article 41
The Security Council may decide what measures not involving the use of armed force are to be employed to give effect to its decisions, and it may call upon the Members of the United Nations to apply such measures. These may include complete or partial interruption of economic relations and of rail, sea, air, postal, telegraphic, radio, and other means of communication, and the severance of diplomatic relations.
Article 42
Should the Security Council consider that measures provided for in Article 41 would be inadequate or have proved to be inadequate, it may take such action by air, sea, or land forces as may be necessary to maintain or restore international peace and security. Such action may include demonstrations, blockade, and other operations by air, sea, or land forces of Members of the United Nations.
The current ICJ court case is about the Convention on the Prevention and Punishment of the Crime of Genocide, which was signed and ratified by both parties. If that is proven, that is the law they are breaking.