When editing the NTFS permissions for some folders on my Windows 2003 Server w/ SP2, I see many accounts like
Account unknown(s-1-5-21-545330648-264140627-1714.....)
This server isn't a member of an Active Directory domain, just a standalone server.
How can I get rid of these orphaned accounts that are showing up?
It's not the orphaned account you need to get rid of, it's the orphaned ACE's. You need to find out if the SID's that are listed are a user SID or one of the well known SID's. You can check it against this list:
http://support.microsoft.com/kb/243330
Also, you can download a utility called SidToName to see if it can be resolved to a user account or to one of the well known SID's. If it doesn't resolve to one of the well known SID's then it's for a user account that doesn't exist anymore (or isn't resolvable) and should be safe to remove from the ACL.