Ironic Title
The title bears an implicit irony. Necklaces are generally endowed as fashionable accoutrement that one chooses to wear as a demonstration of style and to draw attention. The actual necklace to which the title refers, however, is one that Dave is forced to wear, is the opposite of fashionable and rather than drawing attention to style draws unwanted attention which produces mocking laughter.
Comedic Irony
The story-within-the-story is stimulated by John witnessing Julius shed a tear over the ham and then inquiring as to why. Julius asserts that whenever he eats ham he is moved to remember the tragic story of his friend Dave once he’s already consumed about two or three pounds. And, in fact, the tear does not appear until he is ready to eat his sixth slice in John’s kitchen. Considering the wealth of tragedy attached to Dave’s story, the sheer volume of meat that Julius must eat before he starts to studying upon it has to be considered a bit of intentional comedic irony.
Truth-in-Advertising
Dave demonstrates his the elevated intelligence attributed to him by Julius when he engages in a bit of sophisticated manipulation to get out of being punished for having learned to read. Since he learned to read by reading the Bible, he convinces his plantation master that this is a good thing because he has learned and accepted Christian moral tenets such as those against stealing. With this in mind, his being false accused of the crime of stealing a ham and that guilt being readily accepted by his master is painfully ironic.
A Mind Enslaved
John, the framing device narrator, ruminates on Uncle Julius and concludes that he “presented to us the curious psychological spectacle of a mind enslaved long after the shackles had been struck off from the limbs of its possessor.” He arrives at this conclusion because his stories of slavery tales of yore lack are lacking in both regret and indignation which John has concluded are the only two natural means of expression toward having been a slave. Thus, Uncle Julius is determined by John to any ability to convey events from that period of his life with any complexity. When the narrative returns back to the present day framing, however, it is John (and his wife Annie) whom seem to have completely missed any understanding and appreciation for the symbolic and metaphorical richness which pervades throughout the narrative told by Julius, thus ironically revealing John himself to be the one suffering from a mind enslaved.
Tragic Irony
Dave winds up hanging to death inside the smokehouse because in his humiliation he has lost his grip on sanity and given in to the delusion that he actually is a ham. This is an expression of the dehumanizing aspect of being a slave, however, so rather than being a demonstration of a mind in a state of deterioration, it may actually be a demonstration of a mind that has learned to think on a higher level. The madness that Dave manifests is portrayed by Julius as an act of sheer insanity in which a man who believes he has become an actual ham went to the smokehouse and harnessed himself up for curing just was done with real hams. That may be true or it may be the ending is tragically ironic: knowing that there’s not cure for racism, he decided he would rather die than live a life as something less than human.