[dr. F.I.N.]

Пойдет?

Код:

RandomIze;
...
var
  i: Integer;
...
CurrentStrings := TStringList.Create;
CurrentStrings.LoadFromFile(filename);
while CurrentStrings.Count > 0 do
begin
  i := Random(CurrentStrings.Count);
  Memo1.Lines.Add(CurrentString.Strings[i]);
  CurrentStrings.Delete(i);
end;
CurrentStrings.Free;