Meh, I think Chris' lack of hygeine is one of those things that gets blown out of proportion because people take jokes and exaggerations as genuine fact.
I'm sure it's below average, but it's not uniquely terrible. As Marvin says, a lot of his showers are probably going through the motions. But that is better than nothing. And there is probably a bit of a funk to the hoard that gives a little odor to his clothes, which he masks with perfumes.
His "greasy" look is how he is. His hair and skin are naturally greasy looking. He could adress that by using various skin and hair products, but I don't think it is a sign he never cleans himself.
It kind of reminds me of the way he dresses. When he wore his clown shirts, he seemed like a guy who really didn't give a shit about how he looks. Five-oclock shadow, unkempt hair, goodwill clothes. It all kind of tied together.
But now he is trying. The whole cross-dresser phase is a real time and money investment he is putting into his appearance. But the results are so terrible. That's what makes it amusing to me.