How to eliminate odor from under the kitchen sink?

Find the source of the odor, if you cant see where it could possibly be coming from call the plumber. If its a rental, the owner should take care of as it is considered to be a " health and safety " issue. Best of luck !

What kind of odor? Mold odor? Rotten odor? Dead varmint odor?

You need to know what's causing the odor first of all. To give you an idea of what to look for, here are some videos that might help.

https://www.youtube.com/results?search_query=odor+under+kitchen+sink

You MUST find the source of the odor! Covering it up is not the answer! ...this could be a health issue!!

The faucet was leaking. and it was wet under the counter. I got the leak fixed and it is as dry as can be. However, it smelled the same before the leak as it does now. I think it might be a combination of mold and wet wood.

If the leak is fixed, try something like Damp Rid I used that after leak in my bathroom, and it really helped.

I mix baking soda in a box of kitty litter to neutralize and trap odors. Leave it for a couple of days and remove.

You may need to remove and replace any damaged wood. There may be mold under the kickspace of the cabinet. a 50/50 mix of bleach and water cleans mold. A 50/50 mix of vinegar and water will kill mold spores. Drywall and insulation in the wall may have mold growth.