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You can do that with combination of two validation rules:

Vallidation Rule 1

Prevent making any changes when Level equals Archived or Closed. PRIORVALUE seems to be not working here so I used ISCHANGED function. Needed to exclude changes to Level because otherwise it will not allow to enter Archived or Closed

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 unless he is a Sys Admin

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