Irony is a foundational element in this story. All of the above answers exist and there are several others. One additional way irony is used is through the role of the narrator. In theory, he is the one in charge - he is the protagonist of the work. But, Orwell uses his position to show the evils and futility of Imperialism. Orwell notes that he felt sorry for the Burmese people because of the torture they went through at the hands of the British, and hated them at the same time because of the torture they put him through daily. In the end, the man in charge, the protagonist, winds up simply being a puppet on the string of the Burmese people. He shoots the elephant to avoid looking like a fool in front of all of those people instead of being the leader he is supposed to be.
A good question. The primary irony used in "Shooting an Elephant" is situational, though this is supported by tone. The narrator sounds calm and almost detached throughout the piece, even when he's discussing very upsetting events. The essay opens with a discussion of him being hated, yet he seems quite a civilized person, and one of the least likely people to be hated. He wants to help people, but must do so by killing. The essay ends with him saying he was glad the coolie had been killed, because it gave him a legal reason to kill the elephant: he has to be glad someone has been killed, so he can protect people. That's ironic.
"And afterwards I was very glad that the coolie had been killed"(paragraph 13) He holds the position of police officer yet is glad by the death of a Coringhee coolie.
Hope this helps.