Note the last 5 items in the first column, that show zero bytes.
Those are things you're not authorized to read, so will always show zero bytes via OmniDiskSweeper and most similar free apps.
Two that can get large are:
.MobileBackups (Local snaphots), but according to the Storage display, you only have a few MBs of them.
.DocumentRevisions-V101 (the Versions database, containing previous versions of files you've changed with apps that support it (TextEdit, Preview, Numbers and Pages, plus some 3rd-party apps). It doesn't save complete copies, but only the changed "chunks."
You've also got 5.9 GB in private (a hidden system folder). That's fairly large, and is probably some very big log files. See the grreen box in OSX Log Files.
For more info, see Lion's Storage Display and/or Where did my Disk Space go?