Validation Rule to prevent editing record

Your problem is you want to lock the whole record for everyone except System Admins once the level is "Archived" or "Closed". Putting a prior value around your level field will thus not help you, since it is only checking if that specific field has changed.

I would suggest you implement something like this:

1. Create a new checkbox "Record Locked".
2. Create a workflow that sets the checkbox to true once the level is "Archived" or "Closed". Optionally, you'd want to also uncheck this when the level changes again to another value.

3. Update your validation rule so it says:

   AND($Profile.Name <> 'System Administrator', Record_Locked__c = true)