Ethics and relativism

We had a course on ethics, and I found it quite interesting. Interesting enough to make it my first post with 'content'.

Essentially, ethics is about right and wrong. People make judgments all the time about other people, themselves, situations. What is the basis for making these judgments. Are these just opinions, just a like and dislike, or are they justifiable and binding on everyone else? These are probably the most basic questions that pertain to ethical debates. I admit I don't know the answer. Let me however present a reasonable argument from both sides.

The relativist position is that right and wrong are just opinions. There are no moral absolutes and therefore, what is right for one person may be wrong for another. When practiced appropriately, this position is indeed consistent. However, the problem is that it is hardly ever practiced consistently, and in fact, when practiced consistently will lead to conclusions which seem to be absurd. For instance, would the actions of the Nazis under Hitler be 'right' in Germany because that was the practice in Germany at the time? Similarly, if what is practiced in a culture at a moment in time is the right thing to do, then there is no scope to argue against the correctness of practices, and Sati would never be abolished. People tend to use the relativist position for whenever it is convenient and refuse to apply it consistently. Hence it seems irrational.

On the other hand, it is hard to subscribe to absolute moral positions because it does seem that what is the right thing to do would depend on the situation. If there are indeed absolute moral rights and wrongs, what are they? We can probably build a moral code from basic fundamental principles, but the question remains, what are these principles? Why are they fundamental?
Pursuing this line of thought leads us to a comparison with mathematics. There are no proofs for the axioms. The axioms of morality are not well defined though. This would imply that right and wrong are essentially arbitrary!