Are there any symbols in the work? How does the symbolism in the story help us understand its meaning on more than one level?

There are a number of symbols in "The Cask of Amontillado." As with all literary symbols, they give us a much deeper understanding and appreciation of the story and its themes. For example, we have Fortunato's outfit. It is carnival time, and Fortunato is wearing motley, clothing made up of different colors—the kind you would see worn by a court jester or fool. A fool is precisely what Fortunato is.
Montresor, in French, literally means "my treasure." The treasure that the narrator possesses is the revenge he has been waiting so long to carry out on the hapless Fortunato. This gives us some idea of just how precious revenge is to Montresor, which, after all, is what the story is about. This particular symbol is intimately related to the dominant action.
Montresor's family motto is Nemo me impune lacessit, which is Latin for "no one harms me without being punished." This motto, mounted on the family's coat of arms, symbolizes the inherited nature of Montresor's thirst for vengeance. Getting back at people who have wronged you clearly runs in the family. The Montresors are not the kind of people you should ever cross. But Fortunato, ever the fool, does not see this.
The setting of the story itself, the carnival, is symbolic of the sheer madness of Montresor's terrible revenge. Indeed, the carnival season is explicitly described by Poe as one of "supreme madness." What better backdrop could there be to carry out such a heinous act? At carnival time, people throw off their inhibitions to enjoy themselves and have fun; they act differently to how they would normally behave in their ordinary, everyday lives. All of these elements of the carnival are present in Montresor's act of revenge.