In the Statler Brothers’ novelty hit with this title, they mention a couple of things I couldn’t quite make out, even after finding a website that showed the lyrics. Specifically:
Sticks no plugs and aviator caps with flaps that button down;
The Hit Parade, Grape Truade, the Sadie Hawkins Dance,
According to a video on YouTube, the first entry (“Sticks no plugs”) shows an ice-cream stand, and the second (“grape truade”) shows a label on a wooden fruit (grape) crate.
This doesn’t sound right. 
Grape TruAde was a soft drink.
Styx nose plugs were used to keep water out of your nose while swimming. Apparently they don’t exist anymore, and a Google search only brings up references to the lyrics.
“Your [Lucky Strike] Hit Parade” was a radio program from 1935-53 and a TV program from 1950-59. It counted down the top songs as based on record sales, jukebox popularity, radio airplay, sheet music sales, etc. (its exact methods of calculation, and the accuracy thereof, were never revealed). The songs were performed each week by the show’s regulars, which changed many times over the years. Joan Edwards, Dorothy Collins, Gisele MacKenzie and Snooky Lanson are some who are perhaps best remembered for theit Hit Parade years. The beginning of rock music kind of sealed the fate of the franchise, although it did return for a brief summer run in 1974.
Sadie Hawkins Dances were around into the 1970s, at least. After the race in Al Capp’s Li’l Abner; the idea is that the girl gets to ask to boy to go.
Is this still a thing today?
Resurrecting an undead thread here …
The line is indeed “sticks, no plugs” and refers to tobacco … specifically to places that would allow cigarettes (sticks) but not “plugs” of chewing tobacco.
I assume “aviator caps with ear flaps” looked something like this:
Although I am answering this 9 years after you asked, hopefully you will see it.
“Sticks-no plugs” is a term used in marbles. “If your shooter stays inside the circle you can say “sticks-no plugs” and that keeps anyone from knocking your shooter out of the ring.”
Aviator caps with flaps that button down were popular with kids in the 30’s and 40’s. You can see an example of a boy wearing one in the movie, “Christmas Story”.
“Your Hit Parade” (or simply “Hit Parade”) was a radio and TV show about the current musical hits.
Grape Truade is a grape soda like grape Nehi.
A Sadie Hawkins dance is a dance where the girls ask the boys. It is named after a character from Dogpatch in the Lil’ Abner cartoons.
I hope this all helps.
Not to be confused with a Sophie B. Hawkins dance (Community reference).