An incomplete list of terms and phrases which I first heard through parodies, puns, and other shenanigans before I actually knew what they were puns of:
"to liquidate" (when I was a small child): the MGM Wizard of Oz movie, when Dorothy reported that she'd melted the Wicked Witch of the West, and the Wizard wisecracked "You liquidated her, eh?" (actual meaning: to convert an asset into cash/money)
"to whet one's appetite" (when I was a small child): a compilation of the mid-twentieth-century newspaper comic strip Pogo which my grandmother had, which had an exchange that was something like, "We should go for a swim before lunch." "A good idea, it'll wet our appetites." (actual meaning: to do something that will increase your appetite prior to a meal)
"eats like a bird" (small child): A Star Trek bedtime story my mom told me in which Cyrano Jones was trying to sell tribbles which were supposedly safe, which he justified by saying said "it eats like a bird"; someone countered that "birds eat half their own weight." (actual meaning: having a tendency to eat only a small amount)
"to knock (someone) up" (child or teenager): on what I'm pretty sure were multiple occasions, I read logic-puzzles or Encyclopedia Brown-esque mystery-stories (so, logic puzzles again) which hinged on the fact that, as the solutions explained, the British English definition of the phrase is to "knock on (someone)'s door to wake them up"! I didn't know either definition. (American English meaning: to get (someone) pregnant)
the words "chaos" and "emerald" (as a small child): I first encountered the term in Sonic the Hedgehog, regarding the artifacts of absolute power known as the Chaos Emeralds, and when I subsequently encountered the phrase "I thrive on chaos" I got confused. ("chaos": disorder; strife; "emerald": a beryl gemstone typically colored green, but as a loanword in Japanese, エメラルド emerarudo can mean any kind of gem).
"money laundering" (middle school or early high school): in an episode of The Simpsons where mafia boss Fat Tony is hosting a big meeting of mobsters who are visiting overnight, and he says, "If you need money laundered, just set it outside your door. You can pick it up in the morning." (definition: taking money obtained through illegal means, and funnelling it through some misdirection or whatever to make it look as though it was obtained through a legitimate source.)
"roll off (one's) tongue"/"spit it out" (middle school I think): an Animaniacs comic book which had a "useless facts" page, which at one point stated that the scientific name for "hairball" was "trichobezoar", to which Rita and Runt have the exchange "Doesn't exactly roll off your tongue, does it?" "Definitely not, Rita -- you kinda have ta spit it out!" ("roll off the tongue": of words, to be easy to say; "spit it out": to succeed in saying something/to say something brusquely)
"Rubáiyát of Omar Khayyám" - in The Adventures of Rocky and Bullwinkle and Friends, there was a story arc which heavily featured a small toy boat Bullwinkle had uncovered, and the attempts by a Grand Vizier from South Asia to acquire it and bring it back to his ruler; it was made out of rubies and had the name "Omar Khayyam" on the bow: hence, "the Ruby Yacht of Omar Khayyam." (Rubáiyát of Omar Khayyám is the title that Edward Fitzgerald gave to his 1859 translation of a selection of poetry attributed to eleventh-century polymath Omar Khayyam. Who was Persian, not Indian or possibly Pakistani. This is also where I learned what a Grand Vizier was.)
Half the jokes in Wurst Cellar by Wallace Tripp, including the title.