You could probably use some kind of Custom Fields For Authors / Profiles, plugin. One example is
http://wordpress.org/extend/plugins/register-plus/
That one has this feature: "Profile Fields. Want more done sooner? Have new users fill out there entire profile or just bits you need all during registration, you can even make them required. Now includes the abililty to add select, checkbox, radio and textarea fields!"
So you could ask all the character sheet questions, on the form, that the user must fill out when signing-up as a registered user of the site. Then the fields of data would show up on that login name's Profile. So each user's Profile would be their character sheet.
You could hack it more, if you wanted each user to have multiple character sheets under their login name.
Hope this helps. Just an idea, one approach