Olimb started his professional career in 2002 in the NorwegianGET-league, playing for Vålerenga, where he grew up. In the 2006–07 season, he finished second among the point leaders and was influential in winning the second straight Norwegian national championship with Vålerenga.
Assigned to the Blackhawks' American Hockey League affiliate, the Rockford IceHogs, for the entire 2010–11 campaign, Olimb returned to Frölunda HC at season's end signing a two-year contract on April 29, 2011. He would play for Frölunda until the end of the 2014-15 campaign. In his last season with Frölunda, Olimb also competed in the Champions Hockey League with the club: In 13 contests, he scored eight goals and tallied 18 assists en route to 2014-15 Champions Hockey League MVP honors.[3]
On April 15, 2015, he signed for Jokerit of the KHL,[4] and moved on to the Kloten Flyers of the Swiss NLA in December 2015.[5] After spending the remainder of the season with the Flyers, Olimb signed a deal with Sweden's Linköpings HC in April 2016,[6] where he would play alongside his brother Ken André.
On May 24, 2019, having played the previous three seasons in Sweden, Olimb left as a free agent and returned to the DEL in signing a two-year contract with German club, Grizzlys Wolfsburg.[7]