Parodies represent an interesting paradox within the general discipline of songwriting. A good songwriter is not necessarily a good parodist, and vice versa certainly applies too.
I recall an illuminating discussion at a festival songwriting workshop, putting forward several points with which I strongly agree. The theory is that to write a good parody one has first to have a degree of affection and/or respect for the original song, second to be able to closely and intelligently mirror its words and construction, and third to convey a totality of concept with a clear "message" (which may take the form of factual exposition, or satirical commentary, or else just plain playful - but inoffensive - fun with words. And yes, it is possible to skit without taking the p out of the original!).
Far too many so-called parodies are either overly crude (smut for its own cheap sake), or too flimsy to have anything but a very short shelf-life; at the same time, many parodies just don't have the vision to rise above (or bother to creatively expand) an isolated one-liner good-idea buried deep within. I call these Halfway To Parodies, or in the very worst cases Parodies Lost... (puns fully intended!)