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Merging a couple of threads about this question and making the merged thread a sticky.

JKT's answer is spot on - OmniDiskSweeper can only see or delete files that the current user has access to, and it sounds like your user account doesn't have the proper permissions to see the other files on your hard drive.

Those files may be owned by other users, or may be owned by the system itself. (Since Apple wrote the code for the Finder, they trust it with information about your hard drive that they don't trust other applications with.)