Interesting...
In the scientific/mathematical sense, normal refers to the normal probability distribution. This includes 99% of the population, which isn't particularly helpful. I guess when people talk about what's 'normal' in society, they're talking about the average point of view.
However, the average will vary depending on your sampling population. So, if you live in a population who are vegan, that is the average behaviour and it's "normal." If you live in a popuation who are inbred axe-weilding mass murderers with blue noses, that is normal. It depends entirely on who and where you are. (Though Warchild has a point - a version of normality is often imposed by those who rule, which must be confusing for the mass murderers)
I don't have a suitably nerdy definition of Common, I'm afraid

Though in my experience, common sense is often used to describe reactions that are intuitive and practical, rather than mathematically or scientifically based. For example, on a building site, most of the workers may not bother wearing their safety equipment, but it would still be common sense to make sure you wear yours.
Or have I been programmed to think that? [Pause to feel exceptionally paranoid]
I'm off to raid the fridge...