Japanese have no sense of humour in general. Only Japanese comedies that are funny are the ones with ridiculously exaggerated characters and situations (GTO, Golden Boy) or ones with something completely random that you simply don't know what's going on but find it never the less amusing (Potemayo, Cromartie High School). Also, some of the older fanservice comedies were funny, though mostly because of the above mentioned exaggeration.
Japanese parody means usually tossing a bunch of references together and that's it, though that's how parody is everywhere. Usually it's not very funny, but there are exceptions such as Excel Saga.