First off, thats a good question; and  i might be able to answer it. look at how different scented candeles affect you. And you know how dogs just LOVE sniffing at crap. we find it repulsing and that it smells horrible but dogs apparently have a different idea about how the smell reacts to them. same thing going with wolverine; he likes chopping on the cigars the smell doesnt bother him because hes a chain smoker an enhanced nose just doesn't work. 

"First off, thats a good question; and  i might be able to answer it. look at how different scented candeles affect you. And you know how dogs just LOVE sniffing at crap. we find it repulsing and that it smells horrible but dogs apparently have a different idea about how the smell reacts to them. same thing going with wolverine; he likes chopping on the cigars the smell doesnt bother him because hes a chain smoker an enhanced nose just doesn't work.  "

A very interesting point. But I think it also has to do with how people can become accustomed to certain smells and after a while the smells don't effect them as strongly or in the same way. I'm sure when he started they probably bugged the hell out of him. But, over time it probably just lost its potency on him as his body got used to it. Plus I'm sure his healing factor could have something to do with it in some long drawn out complex answer.

speaking of crap, he may smoke cigars to permeate his nostrils so he doesnt smell other more unpleasant things.
remember he can smell everything around...well. so yeah, poop, and...okay you can imagine. but
keep in mind as well, a sense of smell, even a super acute one, cant be turned off and on.

I had not thought about the fact that smoking dulls your sense of smell and taste for that matter which are both connected. 
Being able to smell EVERYTHING would  suck really bad, so I guess you would need to find a way to drown some of them out.

Why does he have heightened sense of smell?

I think it's like how smokers don't know how bad it smells for other people. Like if you are a smoker, you wont notice the smell when you step into a place where someone has been smoking (alot), as a non smoker you know almost immediately when you've been the same place.

@bez616: Because it’s part of his mutation.