We use onions so often, and so quickly, that there's rarely a problem with spoilage. However, when I do have to store an already-cut onion I place it, cut side down, on a piece of Press 'n Seal plastic wrap. Bring all the edges of the wrap up and twist into a "tail" and put the covered onion into a sandwich bag. Never had a problem with onion odor permeating the refrigerator. One thing I like about the Press 'n Seal is that is seals so completely that the onion is almost like freshly-cut when I take it out to use it even after a number of days of storage.
"As a girl I had zero interest in the stove." - Julia Child
This is real inspiration. Look what Julia became!