Please, read my comment to the question. We can't "convert" your sql query to Linq query without seeing the data.
Have a look here:
SqlMethods.DateDiffDay Method[
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LINQ to SQL Tips and Tricks[
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[EDIT 2]
var qry = from a in md
group a by new{Year = a.RecDate.Year, Month = a.RecDate.ToString("MMM"), Dept = a.RelDept} into grp
select new
{
Year = grp.Key.Year,
Month = grp.Key.Month,
Dept = grp.Key.Dept,
AvgIA = grp.Average(g=>(g.RecDate - (g.Intl_Ack !=null ? g.Intl_Ack : DateTime.Today)).Days),
AvgRD = grp.Average(g=>(g.RecDate - (g.Resol_Date !=null ? g.Resol_Date : DateTime.Today)).Days),
SumOp = grp.Sum(g=>g.Status=="Open" ? 1 : 0)
};