고생이 많으십니다.
DBGrid에서 타이틀을 클릭시 Sort하도록 만들었던 겁니다.
참조하시기 바랍니다.

procedure Tfrm.DBGridListTitleClick(Column: TColumn);
begin
  SortGrid(Column);
end;

procedure SortGrid(Column: TColumn);
var
  slSQL : String;
  ilPos,i : integer;
  p_Qry : TQuery;
begin
  p_Qry:=TQuery(TDBGrid(Column.Grid).DataSource.Dataset);
  if not p_Qry.Active then Exit;
  if Column.Field.Calculated then Exit;

  for i:=0 to TDBGrid(Column.Grid).Columns.count-1 do
  begin
    if TDBGrid(Column.Grid).Columns[i]<>Column then
    begin
      if Pos('▲',TDBGrid(Column.Grid).Columns[i].Title.Caption)>0 then
        TDBGrid(Column.Grid).Columns[i].Title.Caption:=
          Copy(TDBGrid(Column.Grid).Columns[i].Title.Caption,
            1,Pos('▲',TDBGrid(Column.Grid).Columns[i].Title.Caption)-1);
      if Pos('▼',TDBGrid(Column.Grid).Columns[i].Title.Caption)>0 then
        TDBGrid(Column.Grid).Columns[i].Title.Caption:=
          Copy(TDBGrid(Column.Grid).Columns[i].Title.Caption,
            1,Pos('▼',TDBGrid(Column.Grid).Columns[i].Title.Caption)-1);
    end; //if
  end;//for
  slSQL := UpperCase(p_qry.SQL.Text);
  ilPos := Pos('ORDER BY',slSQL);
  if ilPos > 0 then
    slSQL := copy(slSQL,1,ilPos+Length('ORDER BY'))
  else slSQL := slSQL+ ' ORDER BY';
    if Column.Field.LookUp then
      slSQL := slSQL +' '+Column.Field.KeyFields
    else slSQL := slSQL +' '+Column.Field.Fieldname;
  if Pos('▼',Column.Title.Caption)>0 then
  begin
    slSQL := slSQL+ ' DESC ';
    Column.Title.Caption:=Copy(Column.Title.Caption,1,Pos('▼',Column.Title.Caption)-1);
    Column.Title.Caption:=Concat(Column.Title.Caption,'▲');
  end
  else if Pos('▲',Column.Title.Caption)>0 then
  begin
    Column.Title.Caption:=Copy(Column.Title.Caption,1,Pos('▲',Column.Title.Caption)-1);
    Column.Title.Caption:=Concat(Column.Title.Caption,'▼');
  end
  else
  begin
    Column.Title.Caption:=Concat(Column.Title.Caption,'▼');
  end;
  p_qry.Close;
  p_qry.SQL.Text := slSQL;
  if p_Qry.Owner is TFrmTzzUpdate then
  p_qry.Open;
end;

AdvStringGrid를 쓰시는게 어떨지요?
물론 Free입니다..구입하면 소스를 제공합니다.
기능은 약간 떨어지나 그런대로 쓸만 합니다.