Listerine mouth wash is quite effective in fighting Gingivitis and Periodontitis. Chewing gum cannot help in that area, nor do most other mouth washes. Toothpaste with fluoride is very good for the tooth enamel and the toothpaste itself helps to wash out particles from the gums and between the teeth.
Salt water is very good for sore throats, but has no effect on most bacteria or viruses.
I have not researched on this subject, but there are some mouth washes which are very effective against viruses, too.