Оформил: DeeCo
Автор: http://www.swissdelphicenter.ch

type
   TMoveSG = class(TCustomGrid); // reveals protected MoveRow procedure 

{...}

 procedure SortGridByCols(Grid: TStringGrid; ColOrder: array of Integer);
 var
   i, j:   Integer;
   Sorted: Boolean;

 function Sort(Row1, Row2: Integer): Integer;
 var
   C: Integer;
 begin
   C      := 0;
   Result := AnsiCompareStr(Grid.Cols[ColOrder[C]][Row1], Grid.Cols[ColOrder[C]][Row2]);
   if Result = 0 then
   begin
     Inc(C);
     while (C <= High(ColOrder)) and (Result = 0) do
     begin
       Result := AnsiCompareStr(Grid.Cols[ColOrder[C]][Row1],
         Grid.Cols[ColOrder[C]][Row2]);
       Inc(C);
     end;
   end;
 end;

 begin
   if SizeOf(ColOrder) div SizeOf(i) <> Grid.ColCount then Exit;

   for i := 0 to High(ColOrder) do
     if (ColOrder[i] < 0) or (ColOrder[i] >= Grid.ColCount) then Exit;

   j := 0;
   Sorted := False;
   repeat
     Inc(j);
     with Grid do
       for i := 0 to RowCount - 2 do
         if Sort(i, i + 1) > 0 then
         begin
           TMoveSG(Grid).MoveRow(i + 1, i);
           Sorted := False;
         end;
   until Sorted or (j = 1000);
   Grid.Repaint;
 end;

 procedure TForm1.Button1Click(Sender: TObject);
 begin
   { Sort rows based on the contents of two or more columns. 
    Sorts first by column 1. If there are duplicate values 
    in column 1, the next sort column is column 2 and so on...}
   SortGridByCols(StringGrid1, [1, 2, 0, 3, 4]);
 end;