International justice is kind of a mess, at least in comparison to domestic justice. For it to be possible for justice to exist, it's not enough to just have a group of people trying to behave ethically to each other. Justice exists when those people organize themselves together in such a way that (semi-) independent institutions emerge. And those institutions -- and the distribution of rights and goods that results from it -- can be just or unjust. I don't think that, at the international level, the relevant sort of institutions actually exist.
Domestic justice works because there are such institutions, clearly institutions, with clear sources of authority. Legislatures, heads of state, judicial bodies, and so on, derive their authority from elections, inheritance, or some sort of vetting process amongst other officials. There's even a robust network of non-governmental organizations which have authority derived from influence or knowledge or even wealth, which are all, at least in theory, secondary to the governmental bodies.
So, whether or not a state is just or unjust is a sensible question. The institutions are there, and either they create and guarantee a robust set of rights, and reasonable distribution of goods, or they don't.
When it comes to the international level, the non-governmental organizations are all there. We have corporations at the domestic and international level; we have universities with domestic but also international significance; media exist both domestically and internationally; and so on. But there isn't much of a world government.
(Okay, fine, the conspiracy-minded like to pretend the United Nations and its affiliated groups are some sort of secret world government. But the UN is so clearly secondary to domestic governments, it's a bit laughable to treat it as a seperate level of government. Rather, it's like an agency or department of the various domestic governments that belong to it.)
The closest there is to a world government is the loos collection of organizations like the IMF and the WTO. Like the UN, the WTO and the IMF -- and so on -- only have authority secondary to the willingness of their members to grant them authority. But unlike the UN, the IMF et al are granted tremendous authority over domestic affairs. So, they are acting as a de facto world government, while not being a government de jure. Officially, they are secondary to domestic authorities. In reality, they exercise tremendous power over domestic governments.
But, they didn't acquire this power through what we generally consider the most central mechanism for acquiring authority, namely the consent of the governed. (Aside: I have problems with this notion, as "consent" is unclear, and rarely given by most of the governed. But that's a detail point.) They acquired it through having power delegated upwards from those we elected to represent us. A delegation which, let's be clear, is of dubious legitimacy itself.
This means that the actions of the domestic governments, who gave up some of their authority, might be just or unjust. But it also means that the actions of the de facto world government are neither. The world government, such as it is, is in a very early stage of development, much as our own domestic governments were centuries ago. So, while one might be inclined to think that the international sphere is thus incredibly unjust, this would be the wrong conclusion. The right conclusion is that there's no such thing as international justice -- at least, not yet.
That is, while there are some institutions which can be evaluated and criticized for their conduct, there isn't really a full organizational framework which can be held to be just or unjust. So, a lot of the criticism of the IMF, WTO, etc. misses the mark. The problem isn't that they're exercising authority. The problem also isn't that they exercise that authority badly. The problem is that their authority is not legitimate. They function more like an aristocracy, deriving their authority from inheritance and favourable position.
In short, given that the non-governmental institutions that exist internationally aren't going away any time soon, we need to improve our world government. We need to make it a real government. This patchwork of institutions we've currently got is a basis, but it needs legitimacy derived directly from the people it governs.
Of course, I have no idea how to actually make that happen. But I figured it was an interesting thought: what if the problem isn't that they have too much power, but that they have power without legitimacy?