Although there are plenty of funny sight gags here, the narrator is actually describing what needs to be done to produce a good victory garden.
Eggs and rubber goods (such as tires) were strictly rationed in WW2, and audiences would have appreciated the reference.
The Italian squash is a caricature of Benito Mussolini.
Barney draws a caricature of Adolf Hitler on the ground in order to have the bombardier squadron hit his garden. Such sight gags were common in wartime cartoons.
On this film's title page, while it is obvious the two carrots form the letter "V" for "Victory", at the bottom the three radishes and the cucumber form the three dots and a dash in Morse Code which stands for the letter "V". The main theme for Beethoven's Fifth Symphony is played at this time which also echos this Morse Code pattern.