Cleaning a heavy plastic storage box?

You may want to check with the manufacturer for the best cleaning solution, but I would start with something like Simple Green.

Is this similar to a deck box, outside?

You could scrub with cleanser and a scrub brush, that should take off the dirt and weathered in grime.

Also try Awesome from the dollar store, that works well.

I would use warm water and just one small squirt of Blue Dawn detergent. Rinse well and if it has odors in it you can use white vinegar and let it sit for an hour or so and rinse

Separate the boxes into lids and bottoms (or drawers and holders, depending on their construction) and give as many of them a little soak as you can at a time, without nesting them inside each other. After 10 minutes, take them out and rinse them, and be sure to dry them well, inside and out.

Do you think that the boxes are stained, or just very dirty?

Unfortunately, depending on the type of plastic the bin is made out of, it can become discoloured and permanently stained, depending on where it has been stored, and what has been stored in it.

Hello. What kind of exposure or stains are problematic? Mold mildew, pine sap, food, oily residue….Posting a photo or more information could be helpful.

What happened to the box?

Wipe with soapy water and microfiber cloth.

Hi! I clean my storage containers outside with soapy water and a microfiber cloth before rinsing with the hose. Dry it out in the sun and it should be freshened up. Good luck!

Power wash it

I would power wash it or use Clorox wipes and then dry with a rag.