The international system set up an international organization in 1945, the UN, to manage issues of peace and security pursuant to certain criteria as defined in the Charter of the United Nations. As a general rule, the charter encourages the peaceful settlement of conflicts, but article 51, for example, does provide for a state to defend itself. The Security Council can use coercive means against a country, as was the case in Iraq in 1990-1991. The legal infrastructure of our international system is the United Nations.
However, as you know, the UN—especially the Security Council—is a political entity. Decisions that are taken by the Security Council are not always based on law or legality. Therefore, some operations happen to be legal, simply because they were voted on by the Security Council, but are considered illegal by some because they do not respect international law. I think that a lawyer could explain this better than I.
As for NATO's presence in Kosovo, the International Commission of Jurists set up by Sweden has declared that the war was illegal, but that it was also legitimate due to the fact that it had garnered the approval of public opinion worldwide. Legitimacy is a much more political concept; it is not based on law.
As for the European Union and the African Union's intervention in certain conflicts, these organizations usually get the green light from the United Nations Security Council. They are covered. Furthermore, the responsibility to protect is a very complicated issue to discuss. Indeed, there are some very strict criteria to be met before this intervention mechanism can be resorted to, otherwise, it would be applied all the time.
As for the volunteer coalition, you are talking of the coalition in Iraq in 2003. From the United Nations' point of view, it was illegal, but in October 2003, a resolution to support a multinational intervention in Iraq gave this intervention legal standing.