At the part right before the tunnel, several Elites will come down from drop pods and one of them will be next to a battlefield methane tank. Stick him with a plasma grenade and he may survive and will be weaponless (even if Mythic is turned off). This may work for any Elite that is next to one.
Go to the level Metropolis in Halo 2 and board the Scarab. Throw a plasma grenade at the Scarab operator Elite while he is operating the Scarab. He will execute the animation for drawing an Energy Sword but will not actually possess one. Easy is the best difficulty for this.
Approach the elevator at the beginning and enter it. When the SpecOps Elite says, "engage active camouflage," stick him with a Plasma Grenade. Because he is invincible while talking, he will perform the berserk animation and then stand there without a weapon. Easy is the best difficulty for this.
Get the Catch and Sputnik skulls and go to the level Gravemind. Make sure that the difficulty is on Easy. Go to the first outdoor area past the Hunters where the Honor Guard Elites and the Brutes are fighting. You should take out the sniper Jackals before attempting to perform this glitch. Get the SpecOps Elite toward the right to throw a plasma grenade at you. Either shoot a Brute Shot at the Elite's feet or jump above his head, but just enough so he does not stick you, and cause him to throw the plasma grenade up in the air. If done correctly, the plasma grenade will land on his head and not you, and he will execute the animation for pulling out an Energy Sword, and again will not actually possess one as this Elite is Special Operations and is not scripted to have a secondary weapon. Instead, he will pull out an invisible Energy Sword and will follow you around the Valley of Tears. When you reach the part where the Flood-controlled In Amber Clad comes, he will not follow you across the light bridge but stand there staring at you.
This glitch is easy to perform, but requires you to be fast. After the Phantom arrives to drop off Rtas, a Spectre and a Spec-Ops Elite, drive the Spectre (or any vehicle) as fast as you can to the Gondola entrance. All of your allies from throughout the level (if they are still alive) will teleport to you once you pass the loading point. If you are fast enough, a strange Elite will appear here who has no weapon and is always a Minor (unless Thunderstorm is on). It is suspected that he is in fact the pilot/gunner of the Phantom that drops off the Spectre for you earlier in the level, and that he takes a while to be erased from the map after leaving the area. This means that if you get to the loading point fast enough, he is teleported to you. He is unresponsive and will not follow you, but he will cry out or leap if you try to run him over.
When the Separatist Phantom arrives to pick up the Arbiter, destroy the Plasma Cannon platform without killing the Elite. Several melees will destroy it as well as a few Energy Sword swipes. If Mythic is turned on, you can destroy it with a few shots from the Fuel Rod Gun without killing the operator. The Elite will have no weapon.
If you exit the map right before the part where you have to get in a Hornet and fight the Scarabs and trigger a loading point, when you reach the secret Elite, look up and to the right and there will be 2 Elites on a higher ledge; they are the ones that operate the Separatist's Phantom's turrets. Use a rocket launcher to bring them down. They will survive the explosion and the fall because they are invincible. They are weaponless. If you have enough sticky grenades, you can arm them with up to 4 weapons.
On any level with Arbiter, support weapons, and a vehicle, if you give him a support weapon then get him in the vehicle, he'll drop it and will be weaponless. Alternatively, use up all the ammo of one of your weapons, kill him, and swap your empty weapon for his and he'll get up without a weapon.
When doing the Half Flood glitch on an Elite, if you move weapons away from the target, it will get up without a weapon.
If you are dual wielding Maulers, then swap one for a Plasma Rifle with an Elite and he will be weaponless.