Symbolism, Imagery, Allegory
Before we talk about any of these symbols, you should know that there are two camps when it comes to interpreting "A Perfect Day for Bananafish." One camp is all about the deep hidden meaning, thinking that every line, perhaps even every word has some carefully chosen significance. From this viewpoint, it matters that Seymour's room is 507, rather than 213. It matters that Seymour's swim trunks are blue. It matters that Sybil likes to eat wax, not jellybeans or pencils. The other camp bases its interpretation largely on the epigraph, which tells us not to approach this story with logic. To pick it apart analytically is to misinterpret Salinger's intentions.
We're going to go ahead and discuss the possible meanings of these different symbols, but keep in mind that it might all be for naught.