how good of an ironic sense of humor does the creature have?

The monster states that his attempt to imitate the beautiful songs of the birds was so awful that he frightened himself into staying quiet. The fact that he could "frighten" himself is an example of his sense of humor.

Sometimes I tried to imitate the pleasant songs of the birds but was unable. Sometimes I wished to express my sensations in my own mode, but the uncouth and inarticulate sounds which broke from me frightened me into silence again.