Plain WH doesn't give me any oily residue feeling. Stirling ben franklin doesn't, either. Yet the lemon chill and iirc the glacial wintergreen does. I've attributed it to the added menthol. (and\or aloe - don't take this as gospel since I'm not in front of my bottle to read the ingredients. So it may not contain aloe.)
Maybe I just got one of the aftershave scents that doesn't give an oily feel or maybe I just didn't notice it. If you can find some type of a pattern maybe it would help some people here out. Either way, we're not all going to like the same things, which is what makes this whole thing fun. It would be so boring if we did.