If you don't have to worry about portability, and the date command installed on your system supports the -d option, this will work:
date -d "May 24 2010" "+%Y/%m/%d"
You can incorporate that with your awk programme to convert your string. I'm not a POSIX expert, but I am fairly certain that this is notstandard at all, so go with caution if you decide on this route.