The Dane, 22, carded a four-under 68, adding to his eight-under 64 from the first round, which had given him a share of the first-round lead.
The afternoon group of the second round is yet to start, with heavy rain on Wednesday meaning the first round was only completed on Thursday.
From those two have completed 36 holes, Oelsen leads Thomas Levet by two strokes after the Frenchman carded a two-under 70. Richard Bland went third at eight-under after hitting a 67.
"I took a lot of confidence from how I played and how I handled the pressure last week,” said Oelsen, who tied for ninth at The Open after pairing with Tiger Woods on the Saturday.