The film's title uses a familiar American phrase that means anything simple or easy, or alternately, a gullible sucker or pushover.
Groucho reportedly provided the following recipe to explain the title: "Take two turkeys, one goose, four cabbages, but no duck, and mix them together. After one taste, you'll duck soup for the rest of your life." - from this review of the movie: filmsite.org
2. About the plot: it's not really supposed to make sense. Of course Margaret Dumont is careless with her money and they go to war for no reason, it's a satire.