At age 42, the relief pitcher is gearing up for his 20th major-league season.
"He's been around for so long. He's seen it all, he's done it all," said Toronto closer Casey Janssen. "He's been an unbelievable sounding board for questions. I mean nobody has it figured out. He's still learning every day as well but he's been through a heck of a lot more than we have.
"Whether it's on the field or off the field, he's been there, done that," added fellow reliever Sergio Santos.
No wonder when Oliver agreed in mid-January to come back for a second season with Toronto, the 29-year-old Santos and 31-year-old Janssen started texting each other.
"We were just so excited, knowing that we have such a big piece in our bullpen coming back," said Santos.
Oliver is entering his second year with the Blue Jays after previous stints with Texas (three times), St. Louis, Boston, Colorado, the New York Mets and Los Angeles Angels.
In 2012, the veteran left-hander went 3-4 with a 2.06 earned-run average, 52 strikeouts and 14 walks over 56.2 innings while setting up Janssen, who took over the closer's role after Santos was injured early on.
After the Jays exercised a US$3-million option for 2013, Oliver took his time mulling over his future. His agent reportedly asked for a renegotiated contract although Oliver distanced himself from that stance.
Oliver has no regrets about coming back, although he admits spring training gets old after 20 years. The season itself can also be a grind mentally.
But asked if it still beats working for a living, he doesn't miss a beat.
"Absolutely ... . There could be a lot of other worse things I could be doing for a living so I'm definitely not complaining," he said.
One factor in his decision to return was Toronto's remake of its roster.
"Winning. It's always about winning," said Oliver. "No question about that."
Oliver, the son of former major league infielder Bob Oliver, says he expects his role with the Jays to remain the same. "Setting up my boy, Casey."
His family — he's married with two kids — calls Texas home but will join him in the summer in Toronto once school is out.
He likes Toronto, calling it a clean city with a lot of good restaurants, and he prefers the summer in the Ontario capital over the searing heat of Texas.
Oliver says it's also easy to blend in in Toronto and live a normal life.
"Nobody really pays attention," he said. "Maybe every now and then but for the most part not really.
"Just throw a hat on and just walk around town and go get some lunch, grab a movie or something. It's not really that bad."
Oliver says good health, good teams and good coaches have helped keep him in the game so long. He's also paid attention, studying opposition batters.
"There's really no magic explanation why I've stayed around so long," he said.
But Oliver does say he knows his body and understands his mechanics.
"He repeats his delivery very well," Janssen said. "He has a good feel for not only his game but also the hitters he's facing. And he knows his strengths and pitches to his strengths."
"It's just a natural ability to throw the baseball where he wants to," added 28-year-old Toronto starter Brandon Morrow. "That's what's got him this far.
"You watch him work and he's not trying to overpower anybody. He's just trying to hit his spot, keep the ball on the ground. He's figured out that works and what works for him.''
Jays manager John Gibbons — starting his second stint at the Toronto helm — is at a loss for an explanation for Oliver's longevity, other than the pitcher keeps delivering.
"He's got a simple delivery, great mechanics, that kind of thing," Gibbons said. "And his role, he's thriving in that role.
"Guys like that, they're rare. It's hard to figure out what it is."
Asked what he will expect when he sends Oliver out, the 50-year-old Gibbons paused and said "Get the hitter out."
"I mean he's done it his whole career, and just from watching in BP (batting practice) and throwing on the side there's still a lot in there. He's one of the most reliable guys in baseball. And we're glad we have him back. That would have been a big hole without him, no doubt."
Oliver, who will turn 43 in October, says he has no plans past this season, at least at this stage.
"Right now I'd say no," he said when asked if he will pitch in 2014. "But things change just like they did last year."
In 716 career games, including 229 starts, he has a 115-94 record with a 4.53 ERA.
As for further down the line, Oliver says he could well stay in baseball although he insists there is "probably a very good chance I won't be a coach when I'm done playing."
"They've got to be at the field so early, and being away from my family again like that wouldn't be fair to them. Maybe when my kids graduate from high school."
But he has not shortage of contacts or experience.
"I'm sure there'll be probably something for me to do in somebody's organization, maybe front office or something like that," he said.
Oliver's kids are 10 and 12.
"They'll be teenagers pretty soon, one of them," he said. "Hey, how about that? Teenagers and (I'm) still playing baseball. Crazy."Suggest a correction