Get rid of the bulk in the strainer,give it a good beat on the bin ,turn it upside down on a rack and we have a spray hose attached to our taps and give it a careful spray through ,a lot of homes have these as well now,and either wash in soapy water or dishwasher this has always worked on sieves,chinois and chronicle strainers ,I have always used a metal sieve as I can pass purrees through it and mashed potato,a fine sieve I would only use for flour so cleaning not a massive issue ,drum sieves you have to take care with drying as they are normally wooden rimmed ,where as tamis sieve you can normally take apart for cleaning,any staining you can use lemon juice or any mild citrus acid cleaner