There's a few issues here.
- By Order of the Emperor can only be used against a monster effect that 'activates' when the monster is Normal Summoned. Obelisk has no effects that trigger from his own or any other monster's Normal Summon. His protective effects are all continuous, and BOotE cannot be used against his Ignition Effect.
- Obelisk's summon cannot be responded to. So even if he did have a Trigger that could activate when he is summoned, BOotE could not chain its effect anyway.
- By Order of the Emperor does not target the monster it is used against though. It is being used against the effect (you do not 'target' effects. Divine Wrath could be used against the activated effect of an untargetable monster).
So to sum up,
By Order of the Emperor cannot be used against Obelisk in any way. Cards like Divine Wrath can be used against Obelisk's Ignition Effect though, they do not target Obelisk.
Yes. Because Obelisk the Tormentor is only protected from card effects that do not target, Tribe-Infecting Virus will be able to destroy Obelisk the Tormentor via its effect.
Yes. Obelisk is only protected from cards that target him. Dark Hole does not target any of the monsters it destroys, even if there is only one. So it will destroy Obelisk.
No, both cards target, and Obelisk cannot be targeted. Use Widespread Ruin instead, it does not target.
Obelisk is only protected from effects that target him, while Ra has no protection at all. Time Wizard can destroy them both.
Attack him with a stronger monster (Honest works well here. Note that Honest does not target Obelisk) - Take control of him with Creature Swap (Does not target) - Destroy him with other non-targeting effects. Smashing Ground, Fissure, Torrential Tribute (can't be used against Obelisk's own summon), Mirror Force, Ally of Justice Catastor, etc. - Deal with him with other non-targeting effects, ie, bounce him to hand with Grand Mole or Legendary Jujitsu Master, or remove him from play with DD Warrior Lady, etc. - If he tries to use his Ignition Effect, you can use Divine Wrath
Divine Wrath can only be used against activated effects - Obelisk has two activated effects, his destroy opposing monsters one, and the trigger that sends him to the graveyard on the turn he was special summoned. Divine Wrath can be used against either of these - note Divine Wrath does not target the monster, so Obelisk's protection effect won't stop it.
Yes. Because Obelisk the Tormentor is only protected from card effects that do not target, Tribe-Infecting Virus will be able to destroy Obelisk the Tormentor via its effect.
Majestic Red Dragon cannot use its effect negation effect against Obelisk the Tormentor because it targets. However its destruction effect when it attacks does not target, and can be used against Obelisk.
Yes. Obelisk is only protected from cards that target him. Dark Hole does not target any of the monsters it destroys, even if there is only one. So it will destroy Obelisk.
The game-legal form of Ra (available only in Japan at the moment) has no protections against being destroyed by effects, whether they target or not. So yes, Obelisk's Ignition Effect can destroy it.
No, both cards target, and Obelisk cannot be targeted. Use Widespread Ruin instead, it does not target.
Judgment Dragon's effect does not target, so it can destroy Obelisk the Tormentor.
Obelisk is only protected from effects that target him, while Ra has no protection at all. Time Wizard can destroy them both.
- Attack him with a stronger monster (Honest works well here. Note that Honest does not target Obelisk) - Take control of him with Creature Swap (Does not target) - Destroy him with other non-targeting effects. Smashing Ground, Fissure, Torrential Tribute (can't be used against Obelisk's own summon), Mirror Force, Ally of Justice Catastor, etc. - Deal with him with other non-targeting effects, ie, bounce him to hand with Grand Mole or Legendary Jujitsu Master, or remove him from play with DD Warrior Lady, etc. - If he tries to use his Ignition Effect, you can use Divine Wrath.
Attack him with a stronger monster (Honest works well here. Note that Honest does not target Obelisk) - Take control of him with Creature Swap (Does not target) - Destroy him with other non-targeting effects. Smashing Ground, Fissure, Torrential Tribute (can't be used against Obelisk's own summon), Mirror Force, Ally of Justice Catastor, etc. - Deal with him with other non-targeting effects, ie, bounce him to hand with Grand Mole or Legendary Jujitsu Master, or remove him from play with DD Warrior Lady, etc. - If he tries to use his Ignition Effect, you can use Divine Wrath
Yes, "Obelisk's" effect can be negate by "Divine Wrath". "Divine Wrath" activates in response to "Obelisk's" effect but does not target the card, it only negates it then destroys it.
Kuriboh's effect does not 'target' the attacking monster. It can therefore be used against the damage dealt by Obelisk the Tormentor, reducing it to 0.