I think that is one of the problems of the movie for most people... the movie was very faithful to the original comics in every way possible. Unfortunately, people are more familiar with the Fleischer shorts, not the comics. Therefore, Sweet Haven is Popeye's natural habitat, not some weird location that he would visit in the Fleischer shorts. And we also get to meet a lot of the major characters of the comics that never made a single appearance in the shorts, such as the entire Oyl family.
So, next time you watch it, keep that in mind: it's not based on the Fleischer cartoons.
Personally, I love the songs -- but I do admit that they take some getting used to. If they ever turned it into a musical for the stage, it would be great for the music to be arranged so that it comes from more natural elements, like the town band and such -- you know, live music on stage. Seems like that's the only way that the oddity of the arrangements.