Meaning: To create a response, position, or statement without planning ahead.
Example: Kennedy's speeches were never on the fly, but always prepared.
Origin: "On the fly" is a shortened version of "flying by the seat of your pants". It refers to flying a plane in response to what is seen and felt through the course of the flight, instead of executing against a prepared flight plan.
Meaning: Abstaining from consumption of alcoholic beverages.
Example: Dean Martin never fell off the wagon. You have to be on the wagon before you can fall off.
Origin: The origin of this seemingly mysterious phrase becomes clear when one learns that the original phrase was "On the water wagon". A water wagon was a common piece of equipment in the days before paved roads. They were used to spray the dirt roads to help control dust.
Meaning: An idea to be considered after one departs, but which won't be discussed now.
Example: Here's one for the road, if a man makes a statement in the woods, and there is no woman around to hear him, is he still wrong?
Origin: The phrase originates from the context of a person having one more (alcoholic) drink for the road. The individual has the drink to make enjoyable the journey ahead, in the same way an interesting question can fuel conversation or thought on a journey.
Example: Every time I see these kids and their baggy pants I can't help but feel over the hill.
Origin: A reference to a journey over a hill. Once you reach the top of the hill and begin your journey down, you have past the midpoint and are on the downside or decline (over the hill). With age, once you have past your peak, you are on the downside (I'll refrain from saying decline).