Halo 3 is stuck inside your Xbox 360 and you want to get it out. There is a way to manually remove it. First you will want to unplug the power for a few minutes to let your Xbox reset. Re-attach the power cord and see if you can now eject your DVD.
If that did not work turn the power off and unplug it. Remove the face plate on you Xbox console. You will need a thick paper clip or something similar. Straighten one end of it out. With the face plate removed you will see 2 small holes right underneath the DVD player and one hole to the right.
Since Xbox uses 3 different DVD drives the procedure will vary. If you have a Samsung or Toshiba drive use the small hole on the right. Should be right underneath the X on the DVD drive faceplate. Push your straightened paper clip in the hole until you feel it hit the gear. The gear needs to be spun from left to right. Poke around until you find it then push in gently until you feel it move. You will see the tray start to move out.
For Hitatchi DVD drives go for the first hole on the left. Beng DVD drives will use the middle hole. This requires the most pressure to get the gear to turn. You will see the tray start to move.
take your time and do not push too hard in case you are missing the correct spot. Once the tray starts to eject you can pull on it slightly to help it open. You should now be able to remove your Game.
Now why did your game get stuck in the first place? Could be a lot of different reasons. You may have to replace your DVD drive if you are having loading problems. See the guide before attempting this.
If you are having other problems with your Xbox 360 Get a copy of the repair manual here.