A:  This one uses four of the bitmaps that come with windows.

unit Bm_outln;

interface

uses Windows, SysUtils, Classes, Graphics, Forms, Controls, StdCtrls,
  Buttons, ExtCtrls, Grids, Outline, Dialogs;

type
  TForm1 = class(TForm)
    Outline1: TOutline;
    Button1: TButton;
    procedure Outline1DrawItem(Control: TWinControl; Index: Integer; Rect: TRect; State: TOwnerDrawState);
    procedure Button1Click(Sender: TObject);
    procedure FormCreate(Sender: TObject);
  private
    bitmaps : array[1..4] of TBitmap;
  end;

var
  Form1: TForm1;

implementation

{$R *.DFM}

procedure TForm1.Outline1DrawItem(Control: TWinControl; Index: Integer;
  Rect: TRect; State: TOwnerDrawState);
var
  VisibleCount,
  ActualIndex: Integer;
  BitMap : TBitMap;
  Offset: Longint;

begin
    {draw on the control canvas, not on the form }
       { Find Item }
  with Control as TOutLine do begin
    VisibleCount := 0;
    for ActualIndex := 1 to ItemCount do begin
      if Items[ActualIndex].IsVisible then inc(VisibleCount);
      if Index = VisibleCount-1 then break;
      end;  { for }

    Bitmap := TBitmap(Items[ActualIndex].data);

    with Canvas do begin
      if Bitmap <> nil then begin
        FillRect(Rect);
        BrushCopy(Bounds(Rect.Left + 2 + (Items[ActualIndex].level-1) * 16,
                         Rect.Top, 16, 16), Bitmap,
                         Bounds(0, 0, Bitmap.Width, Bitmap.Height), clBackGround);
        end;

      if odSelected in State then begin
         Font.Color := clHighLightText;
         Brush.Color := clhighLight;
         end;  { if }

      TextOut(Rect.Left + 5 + (Items[ActualIndex].level) * 16,
        Rect.Top, Items[ActualIndex].Text);
      Font.Color := clWindowText;
      Brush.Color := clWindow;
      end; { with }
    end; { with }
end;

procedure TForm1.Button1Click(Sender: TObject);
begin
  with OutLine1 do begin
    AddObject(0, 'Level 1', Bitmaps[1]);
    AddChildObject(1, 'Level 2', Bitmaps[2]);
    AddChildObject(2, 'Level 3', Bitmaps[3]);
    AddChildObject(3, 'Level 4', Bitmaps[4]);
    AddObject(0, 'Level 1(a)', Bitmaps[1]);
  end;
end;

procedure TForm1.FormCreate(Sender: TObject);
begin
  bitmaps[1] := TBitmap.create;
  bitmaps[2] := TBitmap.create;
  bitmaps[3] := TBitmap.create;
  bitmaps[4] := TBitmap.create;

  bitmaps[1].LoadFromFile('c:\windows\honey.bmp');
  bitmaps[2].LoadFromFile('c:\windows\cars.bmp');
  bitmaps[3].LoadFromFile('c:\windows\tiles.bmp');
  bitmaps[4].LoadFromFile('c:\windows\waves.bmp');
end;

end.

There was a compuserve posting that gave an alternative coding because the above code didn't work for them.  (It works fine for me. <G>)  I am including it here for completeness.

unit Unit1;

interface

uses
  SysUtils, WinTypes, WinProcs, Messages, Classes, Graphics, Controls,
  Forms, Dialogs, DBTables, DB, StdCtrls, Grids, Outline;

type
  TForm1 = class(TForm)
    Outline1: TOutline;
    Button1: TButton;
    procedure Outline1DrawItem(Control: TWinControl; Index: Integer;
      Rect: TRect; State: TOwnerDrawState);

    procedure Button1Click(Sender: TObject);
    procedure FormCreate(Sender: TObject);
  private
    { Private declarations }
  public
    bitmaps: array[1..5] of tbitmap;
    { Public declarations }
  end;

var
  Form1: TForm1;

implementation

{$R *.DFM}

procedure TForm1.Outline1DrawItem(Control: TWinControl; Index: Integer;
  Rect: TRect; State: TOwnerDrawState);
var
  BitMap:    TBitMap;     {for the item's bitmap }
  OffSet, VisibleCount, ActualIndex: Integer;
begin
  {draw on the control canvas, not on the form }
  { Find Item }
  VisibleCount := 0;
   Offset:= 25;
  with OutLine1 do begin
     for ActualIndex := 1 to ItemCount do begin
      if Items[ActualIndex].IsVisible then inc(VisibleCount);
      if Index = VisibleCount-1 then break;
    end;  { for }

    if ActualIndex = ItemCount then exit;
    { rectangle }
    Bitmap := bitmaps[ActualIndex];
    with Canvas do
      if Bitmap <> nil then begin
        BrushCopy(Bounds(Rect.Left + 2+ Items[ActualIndex].level * 10,
              Rect.Top, Bitmap.Width,
              Bitmap.Height), Bitmap,
              Bounds(0, 0, Bitmap.Width, bitmap.Height), clPurple);
{     four pixels between bitmap and text }
        Canvas.TextOut(Rect.Left + Offset + Items[ActualIndex].level * 10, Rect.Top, Items[ActualIndex].Text);
      end;
  end;
end;

procedure TForm1.Button1Click(Sender: TObject);
begin
  with OutLine1 do begin
    AddObject(0, 'Level 1', Bitmaps[1]);
    AddChildObject(1, 'Level 2', Bitmaps[2]);

    AddChildObject(2, 'Level 3', Bitmaps[3]);
    AddChildObject(3, 'Level 4', Bitmaps[4]);
    AddChildObject(4, 'Level 5', Bitmaps[5]);
    AddChildObject(0, 'Level 1(a)', Bitmaps[1]);
    FullExpand;
  end;
end;

procedure TForm1.FormCreate(Sender: TObject);
begin
  chdir(extractFilePath(Paramstr(0)));
  bitmaps[1] := tbitmap.create;
  bitmaps[2] := tbitmap.create;
  bitmaps[3] := tbitmap.create;
  bitmaps[4] := tbitmap.create;
  bitmaps[5] := tbitmap.create;

  bitmaps[1].loadfromfile('bitmap1.bmp');
  bitmaps[2].loadfromfile('bitmap2.bmp');
  bitmaps[3].loadfromfile('bitmap3.bmp');
  bitmaps[4].loadfromfile('bitmap4.bmp');
  bitmaps[5].loadfromfile('bitmap5.bmp');
end;

end.