Caricature, burlesque, parody, travesty are comparable as nouns meaning a grotesque or bizarre imitation of something and as verbs meaning to make such an imitation.
Caricature implies ludicrous exaggeration or distortion (often pictorial) of characteristic or peculiar features (as of a person, a group, or a people) for the sake of satire or ridicule.
Burlesque implies mimicry (especially of words or actions in the theater) that arouses laughter. The term usually also suggests distortion (as by treating a trifling subject in mock-heroic vein or by giving to a serious subject a frivolous or laughable turn) for the sake of the comic effect.
Parody basically denotes a writing in which the language and style of an author or work are closely imitated for comic effect or in ridicule.
Parody, like caricature, may involve exaggeration or, like burlesque, distortion but ordinarily is more subtle and sustained than the first and quieter and less boisterous than the second.
In extended use parody may apply, often with more than a hint of bitterness or disgust, to a feeble or inappropriate imitation or to a poor inadequate substitute.
Travesty is usually a harsher word than others of this group; it implies a palpably extravagant and often debased or grotesque imitation and more often and more intensely than parody suggests repulsion.