In one, over a photograph of the two in conversation, the Vice-President opens with, "I'm gonna throw his wig into the fireplace", a plan Obama discourages. Biden replies: "One horcrux down, six to go", referencing the Harry Potter story.
And so it went, back and forth across the internet, Biden planning to booby trap the White House, or leave clues about Obama's Kenyan birthplace, to trick Trump one way or another.
The meme, often an esoteric and opaque street-level fringe-dweller, had made it to the Oval Office.
Of course, that was last year. The meme has moved on, as it ever does, riding the internet zeitgeist. Here, catchphrases are both born and borne. Accompanied by an image or video, captions (harsh or mirthful) twist the meaning of the original; messages take on new life, or they fizzle and die. It's a landscape where the line between cool and cringe is as thin as a silicon chip.
Memes might seem a relatively new construct, mirroring the rise of various social media platforms, yet the term has been around for four decades, Richard Dawkins having introduced the word in his 1976 bestseller The Selfish Gene. Alongside his idea that the gene is the "fundamental unit of selection, and therefore of self-interest" (as opposed to a species, group or individual), the neo-Darwinian coined a concept about cultural transmission: the meme, or replicator, a unit of imitation.
"Just as genes propagate themselves in the gene pool by leaping from body to body via sperms or eggs, so memes propagate themselves in the meme pool by leaping from brain to brain via a process which, in the broad sense, can be called imitation," Dawkins wrote.
Shortly after this analysis, he characterised God as a meme.
Dawkins' notion of highly dynamic promulgation has mutated into a range of internet outcomes. Examples are wide-ranging, from banal fart-jokes, to Kermit the Frog as Darth Vader, to comments on pop celebrity fashion faux pas, to political contexts made ironic or reimagined.
It's more the playground of the young and culturally nimble than of old fogeys like Dawkins.
In the former category sits Dunedin teenager Reva Grills', who has her own favourite of 2016. Another take on the US election. It involves that first meeting at the White House when Obama shook hands with Trump.
"Obama has this look of horror, while Trump looks like he can't believe what has happened," the former Logan Park High School head girl says, adding she believes Trump is likely to be the focus of many a meme during his first term in office.
The image has been captioned, recaptioned and doctored countless times: some of them are quite rude.
"The point of memes is numerous, whether it be making a comment (usually blunt and humorous), subverting a widely held opinion, or a new mode of discourse ... these are all valid," Reva,18, says.
"But they're often also just wee nuggets of comedy gold that no one's necessarily thought of that randomly appear on social media feeds."
Mark McGuire, a senior lecturer in design (including digital media) at the University of Otago, regards memes as a process rather than a specific form. Think verb versus noun. A meme isn't just an object, image, video or opinion that is shared, Dr McGuire says. Part of what might be termed remix culture, a form of recycling, memes offer myriad social nuances (laughter, sadness, disdain ...) that prompt others to respond, be it to forward the example and/or manipulate it.
"One characteristic of internet-style memes is that there is no central authority controlling them. People can do with them what they like," Dr McGuire says, citing the "Nek Minnit" video, well reported in 2011. Skateboarder Levi Hawken didn't intend to make a video that would go viral; it just did.
"And once something becomes popular, it becomes more popular. It takes on a celebrity status.
"When you look at the evolution of internet memes, they used to be text phrases; then they were images; more recently, they have become videos. And just like other forms of media, they are becoming more conversational."
He points to a more recent example: Texan mother Candace Payne trying on a Chewbacca mask, and laughing hysterically. Uploaded to Facebook in May last year, the video received more than 100 million views in two days. That figure has now risen to more than 165 million.
"More than anything else, it was the laughter that was catchy. It went viral, as they say. However, unlike Levi's video, this mother took control of the popularity of that video and now has a website leveraging off that."
Often a meme is prompted by a news story or incident. It's a response or criticism encapsulated in an image or phrase. Yet, Dr McGuire says, memes travel more effectively if they are underground, so to speak, versus being part of mainstream media discourse.
"Memes are popular in the same way that street culture is popular. Think of the punk movement of the late 1970s. By the time that arrived in New Zealand - or Canada, where I was living at the time - it was more about a fashionable and expensive haircut. Much of its potency had gone because it had been embraced by conventional consumer culture.
"That happens with things that go viral, too. Memes are a 'bottom-up' construct; they have life when they are shared by everyday people. As soon as they are christened by traditional media, they lose their potency."
Oscar Ladell describes a meme, in the broadest sense, as a shared idea.
"It is a joke, concept or piece of media that is shared and used in different contexts. This can be as simple as a funny picture of someone looking angry. This is then applied to other situations, through a caption or, simply, context."
Memes can also be used as a means of cultural alignment, the 18-year-old former Logan Park High School pupil notes. They might find favour within a group comprising just a few friends, or a larger societal sub-group. Oscar cites the example of Pepe the Frog: having first appeared in 2005 in an online cartoon along with the catchphrase, "feels good, man", the meme developed into a subset that featured racist themes.
During the US election campaign, Pepe was transformed into a mascot for the "alt-right", described as a disparate group of far-right Trump supporters, including white power nationalists. In August, Trump re-tweeted a picture of himself as Pepe.
Last year, the US-based Anti-Defamation League established a Save Pepe campaign with the cartoon character's creator Matt Furie in an attempt to reclaim the symbol from those who have used it for hate speech.
"People can become memes," Oscar says.
"Their personality is viewed by others in a similar way to more traditional memes.
"Politicians such as Donald Trump try to create memes by what they say or share. His false statistics about race violence comes to mind. Or they try to make themselves into a meme. By creating such a consistent and extreme personality, Trump has turned himself into a meme that people can reference and use. I believe this has significantly contributed to his success as a politician.
"Politicians also try to capitalise on existing memes to boost their popularity. A perfect example is Hillary Clinton mentioning Pokemon Go in a speech, which was an attempt to endear herself to more people."
The connection between memes and propaganda filters into the paradigm of fake online news, the rise of which last year prompted Barack Obama to rail against an internet ecosystem in which "everything is true and nothing is true".
"In an age where there's so much active misinformation, and it's packaged very well, and it looks the same when you see it on a Facebook page or you turn on your television ... if we can't discriminate between serious arguments and propaganda, then we have problems."
Obama wasn't being paranoid. According to an analysis by Buzzfeed News, fake news outperformed real news on the platform, receiving more shares, reactions and comments.
The cultural influence extends to language too, memes providing inspiration for new words and phrases to take hold.
The Kiwi pride surrounding "Nek Minnit" notwithstanding, there is "on fleek" (loosely translated as "on point" or looking good), introduced by American Peaches Monroee via a Vine video clip she posted in 2014 after addressing the camera from her driver's seat. She was referring to her eyebrows, by the way.
Reva Grills says there are really no rules to memes, although she begs those pondering a post to only do so if it is "funny, witty, or brilliant" (or a combination of those). Otherwise, "don't bother".
Still, it's a free world, she says.
"Just don't go into the meme world thinking you're going to explode and become famous, because most memes' owners are unknown; well in my case, anyway.
"Some lovely people have just created and released these internet gems and are probably all just in the dark with their laptops grinning their chops off, like the rest of us viewing their content.
"There is a range of intellects when it comes to memes: there are hilarious political ones into which someone might insert something intelligent, but a meme doesn't necessarily have to be humorous."
All that viral replication can also serve as an emotional release valve.
Amid the deaths last year of major cultural figures (David Bowie, Prince, Muhammad Ali, among others), the slaying of a hitherto little-known gorilla provided another platform for grief (both genuine and feigned) to be expressed.
Enter (or exit) Harambe, the gorilla shot dead in Cincinnati Zoo in May when a young boy climbed into his enclosure. The primate's death prompted massive controversy; social media pages were set up in his memory, angry tweets sent. Although the clamour eventually dimmed, both online and in more mainstream media, a resurrection of sorts took place. The earnest posts following Harambe's death were tweaked and twisted. A gorilla's fate. Thousands of grins.
In-jokes popped up in all sort of places, including in the Otago Daily Times. A seemingly innocuous article, published in September, about a high school spelling quiz had one teenager dedicating his team's win to the memory of the 17-year-old western lowland gorilla: "We still haven't had justice for Harambe."
Yet, given claims that the fastest way to kill a meme is to write a mainstream media think-piece about one, Harambe may rest in peace after all.
