Use whatever product you would use to clean any pipe (I tend to go with high-proof liquor, followed by a carnuba wax), but apply the cleaner -- gentlty -- with an old soft toothbrush. It will reach into the crevices for any oils or soot and lift them out.
If you do wax after, try using a rougher cloth (like a terry washcloth) than you might normally use, so you don't get any gunky wax buildup in the nooks and crannies.