Years ago I read an article that interviewed top chef's and asked them how to keep an onion in the refrigerator that has been sliced. The answer seemed to be to use a plastic wrap and wrap it tightly to avoid odors and keep the onion fresh.
I remember guffawing and wondering if these 'top chefs' have ever even saved half an onion before in their life? Wrapping an onion in plastic wrap does not stop the odors and does not keep it fresh. The moisture ruins the onion quickly and the scent of onion permeates the open foods around it.
Once again, Grandma knows best. Dig out some old church cookbooks from long ago and read the hints and tips pages. Grandma knew to wrap the onion in aluminum foil and now you do too.
I actually own two 'onion keepers' which are thick plastic, half a circle (half an onion) shaped containers that seal tightly and do keep the scent of the onion from spreading to other foods but they also seal in so much moisture that the onion spoils within a few days. If you are a long time reader of my website you'll know that I love aluminum foil for wrapping my lettuce and celery to keep it fresh for a month... add onions to list of foods to wrap. It's a natural odor barrier and will keep the onion fresh for a week or two.