I think when you mean "sharpen" icons you really mean having them be crisp and clean.
Sharpening your icons will not make it more sharp; or at least not in the way that you're thinking.
There is nothing you can do to this icon to make it clean other than recreating it or finding a proper source for it. This icon is essentially dead.
The main issue with the icon (and what is giving it this weird look) are the uneven widths and distorted edges.
Other than that you need to remember you're working with a 16 x 16 icon. There isn't much "sharp" awesome quality you can punch into it. It is also not advisable to start with a big (raster) icon and scale it down. This will not produce clean results.
Icons should either be created at their desired dimension or be created as a vector so that they can be scaled to fit any size.