When you clean your sink, make sure to give a little extra attention to the sink strainer. However, if your drain is emitting an odor, cleaning the strainer along with the drain is advisable. The strainer is actually set far down into the sink where the drain pipe connects. It is not just the cup that catches food particles inside your sink. If you are interested in cleaning the cup, you can simply run it through the dishwasher on the top rack.
When you clean your sink after use, you can wipe down into the strainer with a soapy rag. This will remove any greasy build-up and will keep the water flowing with ease. Sometimes food particles can collect in the openings of the strainer. If you find the openings full of waste, pick it out with a fork and then wipe down the sides with a grease cutting detergent.
If your drain in smelly, you will have to pour something into the drain to kill the bacteria causing the smell. The strainer will inevitably be treated with this same substance. Once you pour the substance into the drain, make sure to let steaming hot water run for a minute or two. This will keep both the drain and the strainer clean.