He had previously denied sexually assaulting and murdering the 16-year-old girl last year.
In his admission read out in court, Oliver said he grabbed Blochliger around the neck to demobilize her.
Oliver said when she lost consciousness, he dragged her body into nearby bushes to prevent anyone from seeing them.
He said he then robbed her.
Oliver added he tied the victim up, before raping her.
He also confirmed that he throttled the teenager.