Of course there is normality, and each of us achieve it by being ourselves. Normality is by definition something that embraces the standards of a given majority. These standards are entirely dependant of the surrounding society. In the ancient Rome, it was consired acceptable and perfectly normal to feed Christians to lions for the amusement of the people. Thankfully this practice has ceased, and anyone who tries to do it now is imprisoned and at least put to a mental hospital for showing signs of perversion.
Abnormality, on the other hand is defined by minorities. These minorities usually have some attribute the majorities don't understand, and thus, fear. Members of the minorities are labeled abnormal to seperate them from the "normal" people, who themselves belong to some minorities as well. Hypocrisy might not be morally acceptable, but it's certainly normal human behaviour.
We all belong to majorities is some respects, and minorities in others. I'd say that is what normality is all about. If we were to create a person who would represent the average of each of our attributes, s/he would be very abnormal indeed!