Much of it is funny, although a lot of it isn't. This is true of Escape from Monkey Island, the fourth game in the series.
Whereas games like Full Throttle and Grim Fandango emphasized character and story, the Monkey Island games have increasingly leaned toward trying to make you laugh by means of an endless barrage of puns and pop-culture references. In contrast to most LucasArts adventures, the Monkey Island games have always been really over the top.