After using the shaver and rinsing it, are you leaving the foil assembly off of the shaver so everything can dry out? You should never store it assembled when wet as this can lead to all kinds of molds and bacterial growth on the inside.
I recommend cleaning both the foil head and the cutters by soaking them in alcohol initially for at least an hour to kill whatever may be causing the smell. Use 70% Isopropyl alcohol; don't waste your vodka, although that will work as well if it is all you have in the house. After soaking, rinse thoroughly with water, reassemble and then run the razor under the faucet. While running the razor, rub a drop or two of liquid soap (any dish soap will work, but I like Dawn because it is better at dissolving grease and oils) on the foil and then rinse again under running water to wash off the soap. Remove the foil assembly and allow it to air dry while open. Prior to your next use, rub a drop or two of light mineral oil on the foil while running the shaver. You should repeat this entire process every month or so. Instead of light mineral oil, you can spray with Shaver Saver which is a silicone based spray shaver lubricant, but it costs more than light mineral oil. Don't use vegetable oil as it can go rancid.
Once cleaned, you can simply rinse after each use and let it air dry. Once per week, you may want to use a drop of liquid soap while rinsing, then air dry, and then apply a drop or two of light mineral oil to the foils while running the razor prior to shaving the first time after using the soap.
This should keep your shaver clean and well functioning. It will also preserve the life of your foils and cutters.
Happy shaving.