The characters in the novel do a lot of "signifying," that is, making humorous and satirical remarks to each other and about each other. Signifying is part of the African American oral tradition and Hurston uses this device a great deal. For example, Janie says that Joe Starks has a "throne in the seat of his pants, " implying that he is authoritarian and overbearing. At the same time she is making fun of him in a passive aggressive way. The porch sitters often make the same kind of remarks about other townspeople.
Also the outrageous hyperbole of the mule story is both absurd and humorous and would qualify as burlesque.
Zora Neale Hurston's Their Eyes Were Watching God is not a particularly humorous novel, though there are some delightfully humorous moments in the story. Labeling them rather depends upon your precise definitions of the terms you mention, however, as they share some common elements.
In Eatonville, there are several men who are not particularly appealing, yet they attempt to "make moves" on Janie in a suave and smooth manner. They fail miserably, but they are humorous and even burlesque in both word and deed.
Also in Eatonville, the boasting of the town's self-appointed leader is so outrageous that it becomes humorous. This is ironic, for Joe Starks is clearly not the best man in the town and this depiction of him might be considered satire.
Down in the bayou, the scene at the restaurant--and the family which runs it--is rather outrageous, as well. Burlesque may apply here, based on the outrageous actions on a grand scale.
In general terms, the especially exaggerated Negro dialect is spoken by the most humorous characters. The men in Janie's life all have rather absurd moments, as well. This would probably be considered hyperbole--exaggeration used for humorous effect.
The men in the novel are generally more caricatured than the women, and caricatures are humorous depictions of reality--probably closest in definition to parody.