Serving in numerous "reporting" roles on the spoof newscast, but chiefly as senior British correspondent, the Birmingham, England-born Oliver is schoolboyish, poker-faced and emphatic in explaining America to itself (whether the topic is Occupy Wall Street, gun control or the N-word), satisfied that his accent from across the pond makes anything he says, however off-kilter, sound authoritative here in the New World.
Recently Oliver said a simple "yes" to his boss, Jon Stewart, who means to take the summer off to make a feature film and asked Oliver to fill in for him at the "Daily Show" anchor desk.
"I'll say 'yes' to anything he wants me to do," Oliver explains at the "Daily Show" offices in midtown Manhattan. "I owe him so much - he brought me over here (to the U.S.) seven years ago - so I'll do anything he wants, whether it's hosting his show or operating as a drug mule between here and Bogota.
"As it happens," adds Oliver, looking relieved, "what he wanted was just hosting this show."
In the coming months, Stewart will be directing and producing "Rosewater" from his own script based on a book by Iranian journalist Maziar Bahari, who was falsely accused of being a spy and imprisoned by the Iranian government in 2009 while covering Iran's presidential election.
And starting Monday, Oliver will preside on "The Daily Show" (which airs at 11 p.m. EDT Mondays through Thursdays on Comedy Central). He will substitute-anchor for eight weeks of new shows before Stewart's return on Sept. 3.
"He's got all the talents and he's gonna be great," declared Stewart in a separate interview. "And he can handle the speed of it. You want somebody in that position for everybody else on the staff, so they don't feel they have to slow down."
But Oliver has his own assessment of the challenge that awaits him: "You're taking this engine and hoping you can operate it with a lower skill set than the guy who designed it."
In person, Oliver is as witty as he is on camera, but unlike his deadpan TV alter ego, he exhibits a toothy grin, a generous guffaw and a palpable delight in mining ideas for humor.
He jokes that he is trying to get a head start on his new responsibilities by writing scripts ahead of time.
"I'm going to try and get to August, at least, by just predicting: We'll get a Supreme Court decision on gay marriage; we'll guess what that's going to be. We've got a royal baby coming; we'll guess what that's going to be."
Oliver, 36, says his comic style was forged by early exposure to Monty Python and Armando Iannucci, a Scottish farceur who produced radio comedies, the British political TV satire "The Thick of It" and, currently, HBO's "Veep" (and will be a "Daily Show" guest next week).
Seeking his own comic style, Oliver wanted to apply "classic British comedic lunacy to politics, trying to do something stupid with something serious."
But starting out, he was grateful for any joke that might score him a laugh or two.
"When you start standup you are just trying to not leave the stage to the sound of your own footsteps," he says. "You're only thinking, 'How do I get through this with just a soupcon of dignity?'"
Whoa! Oliver has left himself wide open to razzing by his interviewer for using a fancy word like "soupcon." He swiftly replaces it with "iota," but it's too late.
That's Brits for you: Always sounding like they know more than your average Yank.
"They SOUND like they do, and that's the trick," Oliver agrees with a laugh. "But there is nothing more British than simultaneously feeling superior and inferior. You just project one, repress the other."
Still, the record shows that Oliver attended highbrow Cambridge University. Just how smart IS Oliver?
"Smart enough to appear smarter than I am," he reasons. "I was smart enough to get into Cambridge, and I guess I was smart enough to realize that I wasn't as clever as everyone else when I got there. I felt kind of out of place there, and spent most of my time doing comedy rather than academics."
Notably, he became part of the Cambridge Footlights comedy troupe, whose luminous alumni include Sasha Baron Cohen, Hugh Laurie, John Cleese and David Frost.
"That was where I learnt, through failure, to do comedy, which, initially, is re-LENT-less failure," he says rhapsodically - "un-re-MIT-ting failure!"
But that was followed by successful standup gigs and TV appearances across his homeland.
Then Stewart discovered him and brought him to these shores.
"From the day I came to 'The Daily Show' I couldn't imagine not being here," says Oliver. "I really love this job! I can't fathom a time that I won't be working here."
And for the next few weeks he is filling in for the man who not only is his boss, but, to hear him talk, a bona fide mentor.
"You KNOW Jon Stewart is funny," Oliver says. "What you DON'T see is, he's a pretty incredible manager of production as well. He's spent over 10 years making sure this show operates in a certain way. The key thing is to really keep your foot on the throat of this show so that it doesn't just get up and walk away."
He laughs appreciatively. "That's the biggest lesson he's taught me."
Starting Monday, John Oliver is putting his foot down, and keeping it funny.