When does oxidation destroy prions?
Prions are fairly resistant to traditional method of sterilization.

Citing from: Guideline for Disinfection and Sterilization of Prion-Contaminated Medical Instruments


  The prions that cause CJD and other TSEs exhibit an unusual resistance to conventional chemical and physical decontamination methods. Because the CJD agent is not readily inactivated by means of conventional disinfection and sterilization procedures and because of the invariably fatal outcome of CJD, the procedures for disinfection and sterilization of the CJD prion have been both cautious and controversial for many years.


The same paper also lists several effective and ineffective methods for sterilization (efficient method have > 3log10 reduction in prion content within 1 hour)
I am not going to list them all here but you can see Table 2 in the paper.

Just to answer your specific question about oxydation, certain oxydising agents are effective, others are not. Similarly certain autoclaving (=sterilising with heat) procedures are fine and others are not.

Another interesting paper Methods to Minimize the Risks of Creutzfeldt-Jakob Disease Transmission by Surgical Procedures: Where to Set the Standard?