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;