Elvarg's head is obtained during the Dragon Slayerquest and is taken from the dead body of Elvarg, the boss of the quest. It needs to be taken to Oziach to finish the quest. It should be noted, that if the player dies after killing Elvarg, and thus drops the head, they can still finish the quest.
Up until 2007, it was not required to return to Oziach with the head. All that was necessary was for players to kill Elvarg. Defeating the dragon would result in the player being teleported out of the room and receiving the "Quest Complete" message as well as the rewards.
When fighting Elvarg, if someone has already taken away over half of her life points, a player will not receive the head. The player that does the greatest damage receives the head. Before the updates, however, this was not the case.
If one puts the head in their bank and finishes the quest without giving the head to Oziach, the head will disappear from the bank.