After receiving the quest go to the Orc Tavern and speak to the bartender, Hershel.
You can persuade Hershel to give you his key to the Chest in the Inn basement by winning the RPS game for 5100 Charisma XP with 4080 XP for the quest update.
Enter the tavern basement and find the chest nearby. The chest is trapped, but doesn't cause much damage which also can be avoided with fire protection. Open the chest (or brute force break it if you failed the previous RPS game) and pick up the Armoury Key for a quest update of 4080 XP.
You may return to confront Hershel about the trap with the following options:
Accuse him of trying to kill you for Vindictive +1 and 3150 XP. Then he will attack you.
Depending on your character's dialogue afterwards Compassionate +1 or Heartless +1
Or forgive him for Forgiving +1 and +25 Attitude
The quest can now be resolved in several ways:
Siding with Lieutenant Gural:
(Optional) Speak to Grutilda and decide not to tell her anything for Independent +1
Return the Armoury Key to Lieutenant Gural at Glen's House for Altruistic +1 and +50 Attitude with Gural. The quest is completed for 8160 XP
Siding with Grutilda:
(Optional) Speak to Lieutenant Gural and decide not to give him the key for Egoistical +1 and -50 Attitude with Gural.
Turn the Armoury Key over to Grutilda and start conflict for Obedient +1 and +35 Attitude with Grutilda. The quest is completed for 8160 XP and Grutilda will go to Gural, talk to and execute him. He will not drop anything, but his body can be looted at the gallows for standard orc corpse loot, no gear.
Keeping the key:
Possible bug: Choose to keep the Armory Key, enter the prison and clear the guards there, and unlock the magic, glowing lock on the armory (room with two chests) earning 4080 Exploration XP. This quest will not be resolved until the final conflict ends at Hunter's Edge, so it will remain in the quest log for a while. You cannot turn in the key if you've already used it to enter the armory. (There is currently a glitch where if you unlock the gate with the guards still alive the door cannot be opened, but the key can still be given to one of those above and finish the quest).
NOTE: As of Enhanced Edition 22.214.171.1240, there is no more bug where the quest can no longer be completed. You can simply use the key to unlock the Armory door, loot the entire room and gain 4080 exploration XP, and then turn in the key to either Gural or Grutilda and finish the quest.