Why don't you give those people warnings, and block them if they don't heed the warnings? Not only this wiki, other wikia also had sockpuppets. All the admins do is blocking them for excessive vandalism.
You discuss with your fellow admins about how to deal with sockpuppets. If those people add in false information or anything that is not acceptable, undo the edits and give them warning. For the case of Jimmy's page (you said that people kept vandalizing it), give them first and only warning. If they done again, block them immediately. For protection of pages, please protect for one day will do. It's up for you to decide. Like I said, discuss with your fellow admins.
Hi, a user keeps vandalizing pages. I keep trying to undo his edits but he keeps on vandalizng. This is getting out of hand and I think an admin should step in and ban the user. Also, he added images that are both inappropriate and irrelvenat to this wiki.