How can I clean out bad odors from kitchen sink drains?

Assuming they are draining ok, I would dump about a quarter cup of baking soda and then pour vinegar over it. Once the baking soda has dissolved, run hot water down the drain.

Bad odor could also be from no water in the P-trap under the sink especially if you've been on vacation allowing sewer odors to come into your home. Run water awhile to fill it back up, or remove it to see if you have a clog.... https://www.youtube.com/watch?v=8PI0iaIB6-4

Put lemon or orange peels in it. Cleans the blades and leaves it great smelling

pour lemon juice and baking soda down the drain and flush with hot water