Kitchen Odour

Sometimes food can get trapped in the garbage disposal. You can put fresh lemon slices down in there and run the disposal. It will break up the food and deodorize. There are other "homemade" recipes that you can use with the same results or you can purchase disposal cleaners (I use them every few months and the homemade recipes between).

Do you know where it's generating from? It could be mold somewhere from wetness under the fridge, etc.

Have you looked in all food pantries and the fridge etc. for old food?

You should not keep the food out of the fridge for longer time even that causes odour. Try keeping the windows open.
Kitchen Faucets

Can you be more descriptive about the odour? "Nasty" can cover a wide variety of things...any parent will testify to that!

Basically you must keep your kitchen clean, you will never have any odour problem. I have recently installed Oak kitchen cabinets and as the cabinets are new they have a chemical like smell. I usually burn an incense in the morning which eliminates the smell and purify the air by giving an aromatic fragrance.