Your spec is a bit vague but such sounds like a custom app is needed with some database server on your server. Does not at this point sound trivial.
My office needs task management software that allows multi-user real-time changes with all the basic features (prioritization, deadlines, etc).
Even a blank googledocs spreadsheet would work, but the problem is that we need this to be secure and off-line behind our secure server's firewall.
My coworkers have tried to use Microsoft Outlook's "Tasks", but they didn't like the fact that it forced them to assign tasks to specific people. Also, I did see that GoogleDocs can be run offline, but i'm not sure how that works or if that would meet our needs.
Does anyone have any suggestions for a free software that would work for us?