I also opened the info dialog for each individual directory under my hard drive, and the total file sizes were under half of what 'About this Mac' -> 'Storage' was showing. running the 'du' command in terminal returned the same results. I can't imagine Omni doing something so different that it returned different results.
Did you run 'du' with 'sudo'?
sudo du /
Otherwise you did not see any files that your account did have permissions to view. For that matter, did you start at top of the directory tree, or just in your home folder?
The MacObserver.com link explained how to run OmniDiskSweeper as root so it would be able to see everything on your disk (the technique could be used for other GUI based file checking utilities). The use of 'sudo' with 'du' is essentially doing the same thing. Making sure you see everything.
I am an experienced developer, and have no problem playing with files and permissions, but that is not relevant. What I'm looking for here are ideas about the differential between the sizes of files on my hard drive and the amount of space that the OS thought I was using.
The Finder information is generally based on Spotlight data. Sometimes re-indexing Spotlight will get things back in alignment.
<Spotlight: How to re-index folders or volumes - Apple Support>
The nice thing about utilities such as OmniDiskSweeper is it shows files everywhere (especially if it is started as a root owned process). Runaway log files have been known to eat up space.
If you are running Time Machine and do not have your storage device attached or accessible (a Time Capsule back home while you are away), then Time Machine takes local snapshots which it will flush to the backup disk when it becomes available. The Finder does not report this information, as Time Machine snapshots will be deleted if the space is needed (or that is the theory). These snapshots can be disabled.
<About Time Machine local snapshots - Apple Support>
I have no reason to delete files in ~/Library. The files in my home directory were taking up only ~150gb, which should have left 250gb free, but didn't. I also had no reason to delete files outside of ~/.
That is "Boiler Plate" because OmniDiskSweeper shows lots of files that many users have never seen before, and deciding they do not need 'mach_kernel' results in a system that will not boot. So I include my warnings anytime I mention OmniDiskSweeper.