It's strange to get different results because PetaPoco it's only running the query through ADO.net, but you can solve the problem ordering by the expression (not the column name) as was done in older SQL versions:
SELECT strGet.StrengthId as AreaId, strGet.[Description] as AreaName,
(SELECT SUM(ias.Score) FROM ImprovementAreaScore ias WHERE ias.StrengthId=strGet.StrengthId) as AreaPriority
FROM
{0}.Strength strGet
WHERE
strGet.[Description] like '%' + @0 and strGet.SelfAssessmentId=@1 and strGet.IsStrength=0 and strGet.ToImprovementProject=1
ORDER BY (SELECT SUM(ias.Score) FROM ImprovementAreaScore ias WHERE ias.StrengthId=strGet.StrengthId)",