I really haven't done research on mouthwash because when our dentist said that our bad breath had nothing to do with local infections or bad teeth, then I knew that the odor was coming from the intestines and possibly due to incomplete digestion leaving food at a smelly stage of the digestive process. Then if some of the toxins produced by this incomplete digestion is absorbed into the blood stream, then it travels to all parts of your body making your body secretions, sweat, saliva, mucous membranes in your mouth, urine, etc., smell as well.
I understand that baking soda takes away odors, and an old remedy used to take away food odors in the refrigerator is to put a small box of baking soda hidden away in a corner toward the back of the refrigerator. Have you ever done that? I have when I've stored fish overnight in a sealed container. The smell somehow seeps through sometimes, and the baking soda takes away the RESIDUAL odor after I've removed the fish from the refrigerator.
I read a post somewhere that a forum member adds baking soda to her normal toothpaste before she puts it in her mouth. I would think that would help. So I would also say that toothpastes that contain baking soday may help with localized mouth odors, but nonetheless, if the odor comes from your intestines, then making sure that you are not constipated and that you are thoroughly evacuating your intestines regularly would help remove the smelly stuff.
I think that just cleaning your mouth well after you eat, brushing your teeth to make sure that bacteria doesn't grow there, and washing and rinsing (gargling) away the smell of the food you just ate helps the scent of your food not mix with the odor coming from your digestive tract, if that is indeed the source of you odor.
Hope this helps. Let us know how it goes for you.