If you have a handle that has pores (like wood), what you are smelling could be rancid oil.
It is strongly advised against using things like olive oil, vegetable oil, etc. on cutting boards because these oils do go rancid and it will ruin the board. I've smelled it myself and it does have a noticeable odor. And for this reason, something like mineral oil is advised for usage.
If this is the case, the problem is that options are limited short of refinishing that actually removes some of the materials. A strong degreaser like dish soap scrubbed in with a brush, and sealing the handle with beeswax after it dries (which you can put on the blade too) may reduce the smell. Prior to removing the coating, this may be easier to start at as it is much less invasive.
Lemons with salt are an excellent polish for many materials (especially for brass and copper), and they do help with smells a good bit. However, this does scratch certain finishes and probably will in this case.
If it is the coating itself, removal and then forcing a patina with something like mustard or grapefruit could help.