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If washing in a washing machine, make sure the dishes are placed on the uppermost dishwasher rack to avoid exposing the plastic to high temperatures. Rinse and dry before continuing. Sunlight has a bleaching effect on plastic, and a few hours of exposure can remove stains, and will help deodorize your plastic dishes. Leave your dishes stain side up in front of an open window, or in a suitable outdoor location where sunlight is plentiful. After a few hours, check to see if the stains have lifted. Baking soda and vinegar are convenient options, and are effective at dissolving many common varieties of food stains. Either soak your plastic dishes in a solution of baking soda, vinegar and warm water (roughly 1 tbsp each of baking soda and vinegar for every cup of water) for 1-2 hours, or scrub the dish using a baking soda paste (made by combining a small amount of baking soda with just enough vinegar or water to make it sticky).  Alternately, you can use salt and lemon juice, instead of baking soda and vinegar, to create a scrubbing paste. Another common household alternative to baking soda and vinegar is rubbing alcohol, which can be applied via soaking, or simply by scrubbing the alcohol into the affected area of the plastic dish. These products can be surprisingly effective at lifting stains out of plastic dishes, especially cups and bowls. Simply fill the cup or bowl with water and drop two denture cleaner or antacid tablets inside, and soak overnight before washing and rinsing. Bleach is potent and somewhat hazardous, but is a good last-resort when other approaches have failed to remove stains. Carefully combine bleach and water at a ratio of roughly one part bleach per two parts water, then allow the plastic dishes to soak in the solution for 30 minutes, then thoroughly rinse the dishes.  Bleach is a very caustic substance, and you should be sure to wear rubber gloves to protect your hands from contact with it. Also make sure the space you are working in is well ventilated, so that the fumes produced by the bleach are safely dissipated.

Summary:
Wash dishes thoroughly to ensure that no food remains on their surfaces. Set the dishes in strong sunlight for at least two hours. Try applying a solution of baking soda and vinegar. Try using an oxygenating agent, like denture cleaner or a fizzing antacid tablet. Soak the dishes in a solution of chlorine bleach.