Windows (NTFS) file permissions are stored in Access Control Lists (ACL) which are made up of Access Control Entries (ACE). Each ACE is valid for a specific user or group.
When you install a new OS and attach an previously existing drive you may see ACEs for users with a name such as S-1-5-21-12345678-....
Every user/group has a unique internal Id, called the SID, these SIDs are stored in the ACEs.
When displaying permissions to a file, the OS takes the SID and looks up the name for it.
Because you set permissions on files with a different OS, the SIDs used do not exist on the current OS and the system can't resolve the names (so it displays the SIDs).
This should explain why you can not access the files, the users with permissions simple do not exist in your current installation.
To work around this problem, you can either use a Windows Domain, which is most likely overkill, or you can only use well-known groups for your permissions.
Well-known groups have the same SID on every Windows OS, so even if you install a new Windows, the SIDs used in the ACEs do exist and work.
Some well known-groups are everyone, users
or administrators
To see more well known groups on your OS, open a PowerShell and run:
get-wmiobject -class "win32_account" -namespace "root\cimv2" | where-object{$_.sidtype -eq 4} | where-object{$_.sid.length -lt 15} | sort name | format-table name, sid -autosize
it shows something like this:
Access Control Assistance Operators S-1-5-32-579
Administrators S-1-5-32-544
Backup Operators S-1-5-32-551
Cryptographic Operators S-1-5-32-569
Distributed COM Users S-1-5-32-562
Event Log Readers S-1-5-32-573
Guests S-1-5-32-546
Hyper-V Administrators S-1-5-32-578
IIS_IUSRS S-1-5-32-568
Network Configuration Operators S-1-5-32-556
Performance Log Users S-1-5-32-559
Performance Monitor Users S-1-5-32-558
Power Users S-1-5-32-547
Remote Desktop Users S-1-5-32-555
Remote Management Users S-1-5-32-580
Replicator S-1-5-32-552
Users S-1-5-32-545
Not all these groups are good candidates to be used for NTFS permissions, because they give their members additional (unwanted) permissions/rights or their membership is only applied when running as an elevated process (Administrators, Power Users).
If the users
group does not work for you, you could use the Replicator
group because as far as I know, it doesn't have any side-effects to its members.