I live in Canada and don't have to worry about moths, so I am no help there. But I have used plastic bins for my baby clothes, and my maternity clothes too. I tried the rubbermade brand and they made the clothes smell, even with ceder blocks. I use the Sterilite brand and they work great. No ceder needed. No smell.
Even if you wash everything expect to find a few items with yellow stains on them when you open the box back up.