It was a good start to the night for the Hoosiers, with Cody Zeller going to the Charlotte Bobcats two places after Oladipo.
Kansas guard Ben McLemore, another player who was considered a potential top-three pick, also dropped, going seventh to Sacramento.
Headed by a lackluster class, the draft promised confusion and second-guessing, with no consensus No. 1 pick and little agreement among the order of the top five.
And with lesser-known names in the draft, veterans soaked up the spotlight in the hours leading up to it.
Yahoo Sports first reported that the Nets and Celtics were working on a trade that would complete the breakup of the Celtics' veteran core.
ESPN reported earlier Thursday that Dwight Howard was unlikely to return to the Los Angeles Lakers when he becomes a free agent next month.
The guys coming into the league were glad for the attention they did finally get once their names were called.
"It's like a weight vest you took off after running five miles," Oladipo said. "It's relaxing, man. But at the same time, you know it's just getting started."
National player of the year Trey Burke of Michigan also was traded, the Minnesota Timberwolves sending his rights to Utah for the rights to Shabazz Muhammad and Gorgui Dieng, the Nos. 14 and 21 picks.
Lehigh's C.J. McCollum rounded out the top 10 by going to Portland.
Stern, retiring in February, seemed to play up the boos, which turned to cheers after every pick, fans perhaps as puzzled as some of the players at the names they were hearing.
"I was just kidding my agent because he didn't bail me out," Zeller said. "He didn't tell me. I didn't know until David Stern announced it. It's a crazy process not knowing, but I'm definitely excited that I ended up with the Bobcats."
Other players couldn't get too excited about their new addresses, because they changed quickly.
Stern was announcing deals by the middle of the first round and they promised to keep coming after he called it a night and turned things over to Deputy Commissioner Adam Silver for the final 30 picks.
The flurry of trades wasn't surprising with so much uncertainty surrounding this class and so much hope in other areas. Teams such as Houston, Dallas and Atlanta already have an eye on Howard's future, needing to have necessary salary cap space to offer a maximum contract that could lure him away from Los Angeles.
The 2014 class — which could be topped by a second straight Canadian in incoming Kansas freshman Andrew Wiggins — will be higher regarded than this one, with James perhaps heading the available free agents to follow.
Local fans seemed pleased with their picks, cheering loudly when the Nets took Duke forward Mason Plumlee at No. 22 and the New York Knicks grabbed Michigan's Tim Hardaway Jr. two picks later.
Stern made his final pick to close the first round to cheers of "David! David!" before handing things off to Silver.