<<I often feel I have an over-developed sense of justice...>>

Or perhaps only an over-developed sense of expectation that justice will be done.

<<But how do we know WE are right, when we say of something, "That's just not right.."?>>

When you pose the question abstractly that way, you are moralizing. I don't mean that perjoratively, only that, in the absence of a concrete instance, the question will yield a general answer that will tend -- to appear, at least -- to be absolute. I think, when speaking of ethics, it may be helpful to ask about particular instances of perceived rights and wrongs and see what general rules or observations might develop from that.

Ultimately, I think, almost any sense of what is right will devolve [upon?] power.