You could use a Common Table Expression to create the SUM first, join it to the table, and then use the WHEN to to get the value from the CTE or the original table as necessary.
WITH PercentageOfTotal (Id, Percentage)
AS
(
SELECT Id, (cnt / SUM(AreaId)) FROM dbo.MyTable GROUP BY Id
)
SELECT
CASE
WHEN o.TotalType = 'Average' THEN r.avgscore
WHEN o.TotalType = 'PercentOfTot' THEN pt.Percentage
ELSE o.cnt
END AS [displayscore]
FROM PercentageOfTotal pt
JOIN dbo.MyTable t ON pt.Id = t.Id