You can do that with a combination of two validation rules working on current fields

Vallidation Rule 1
------------------
Prevent making any changes when Level equals Archived or Closed unless User is a Sys Admin. Needed to exclude situation when changes are done to Level because otherwise it will not allow to enter Archived or Closed. `PRIORVALUE` seems to not work here so I used `ISCHANGED` function to capture that. 

    AND(
       $Profile.Name <> 'System Administrator',
       NOT(ISCHANGED(Level__c)),
       OR(
          ISPICKVAL(Level__c, 'Archived'),
          ISPICKVAL(Level__c, 'Closed')
       )
    )

The thing is that this rules allows making changes if User at the same time changes `Level__c`. That's why we need second Validation rule.

Vallidation Rule 2
------------------
Prevents User from changing Level__c once it is Archived or Closed, unless he is a Sys Admin

    AND(
       $Profile.Name <> 'System Administrator',
       ISCHANGED(Level__c),
       OR(
          ISPICKVAL(PRIORVALUE(Level__c), 'Archived'),
          ISPICKVAL(PRIORVALUE(Level__c), 'Closed')
       )
    )