Rabbits don't generally eat onions - the sulferous smell deters them. In fact, vets recommend against feeding pet rabbits onions, which can sicken them. Some garden forums suggest planting onions to deter rabbits. Several university extensions also suggest that rabbits do avoid onions.
For a good list of plants rabbits like (and dislike) you can visit http://www.rabbitscram.com/Plants%20Dam ... abbits.pdf
Their list was complied form Ohio State.
Squirrels also generally dislike any alliums - onions or garlic. But suirrels may dig in loose earth and seem to be disturbing the bulbs.
Both creatures MAY nibble the above ground greenery, but it appears they usually don't like onions at all.