type
  TStrColor = class(TObject)
  public
    Color: TColor; {вы могли бы также определить частные и
    публичные методы доступа}
  end;
...

procedure TForm1.FormCreate(Sender: TObject)
var
  i, j: Integer;
begin
  with StringList1 do
    for i := 0 to ColCount - 1
      for j := 0 to RowCount - 1
      Objects[i, j] := TStrColor.Create;
end;
...

procedure TForm1.StringGrid1DrawCell(Sender: TObject; Col, Row: Longint;
  Rect: TRect; State: TGridDrawState);
var
  OldColor: TColor;
begin
  with StringGrid1.Canvas do
  begin
    OldColor := Font.Color;
    Font.Color := (StringGrid1.Objects[col, row] as TStrColor).Color;
    TextOut(Rect.Left + 2, Rect.Top + 2, StringGrid1.Cells[Col, Row]);
    Font.Color := OldColor;
  end;
end;
...

procedure TForm1.ProcessSelection(Sender: TObject);
var
  i, j: Integer;
begin
  with StringGrid1.Selection do
    for i := left to right do
      for j := top to bottom do
        MessageDlg(IntToStr(i) + ',' + IntToStr(j) + '-' +
          IntToStr((StringGrid1.Objects[i, j] as TStrColor).Color),
          mtInformation, [mbOk], 0);
end;