Oliver remained a hostage until Jason was taken to radiology. Once Jason handed over his gun, the other hostages ran, leaving a curious Oliver with House and Thirteen. Oliver also had become obsessed with what was wrong with Jason. However, he regretted his decision when after the scan failed to find the problem, House handed the gun back to Jason. However, Oliver did manage to escape soon after.
Character page at IMDB (Note, this page overlaps other characters named "Oliver" on the series.