You can get an attachment for your hose that will create more pressure for a faux pressure washer effect, and that works fairly well for plastic lawn furniture.
Peg: You can rent a power washer at Home Depot!
I use a power washer or a bucket full of warm sudsy water with Dawn dish soap and a firm bristle scrub brush to scrub away the dirt and grime. You can also use some Tilex spray mold and mildew remover if you have some tough mildew stains.
I would just use a cleaner dissolved in water and wash them down, followed by a clear water rinse from the garden hose. Tough dirt may need sink cleanser (Ajax, etc.) or an Mr. Clean eraser. You can also paint them with spray paint designed for plastic.
This solution works great for outdoor plastic furniture: https://amzn.to/2THPArv
Hope this Helps! Jeremy - https://pahjodesigns.com
Windex makes a special cleaner for outdoor furniture
We use Simple Green and a hose. If it's really really dirty we have used our power washer. You can get the Simple Green at Home Depot or Lowe's.
I spray mine with diluted blue dawn then hit with a high pressure hose.
I use Simple Green, scrub them down then hose them off