I'm not sure there is just one literary device at work here. There are several poetic devices used.
Because it is Shel Silverstein (a children's poet) you should automatically look for the humor. Nearly all of Silverstein's poetry is written with a tone of childish, lighthearted humor. This poem is no different.
The poem, though short, is full of "messy room" imagery. In fact, the room is described as "mucky" and "damp," and there is a "lizard" in the bed. It is almost as if this room has turned into a swamp of mess.
The humor could actually be classified as irony at the end. The speaker is quite descriptive about the state of the room, asking over and over whose room it is. Ironically (but not unexpectedly), it turns out it is the speaker's room. He has just given a rather embarrassing explanation of his own filth, which was at such a repulsive level that he apparently didn't even recognize his own room through it.