Is there a way to go through and create a report (either in Civi or using Drupal Views) that shows what records have been updated by the owner themselves? Such as them going in and updating an employer or address?
There is no such report that filters by logged in user and no integration with views as well AFAIK.
If you want detailed change log than you (system has logging enabled) then you can use Extended logging report. And manipulate report parameter like
If you don't have logging enabled than you can use Database log report and build report parameter
If you want to support filtering by logged in user in one of the two above report than you add filter using selectWhereClause or alterReportVar hook.
Support to views won't be difficult by writing an module extending to civicrm entity module. If you can extend views module to support change log than you can filter or retrieve various data of the contact.