It seems like a no-brainer than oxidation, playing the, er, role it does in the universe, would destroy prions just like it destroys everything else.
But when does it do that? I assume this has been studied, since people handle them in laboratories and may need to sterilize their instruments.
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?
If you google "prion oxidation" you'll see that there has been some research into this over the last 10 years, though it seems to be a minor focus of the overall field. There seems to be some interest currently in using ozone to inactivate prions. One company that offers a ozone-based sterilizer claims to be testing for effectiveness against prions, but that is an extremely long-term process (you have to isolate prions, subject them to your sterilization process, then inject them into the brains of mice or hamsters and wait to see if disease develops).
If you're curious as to how researchers sterilize material in the lab, I may be able to shed some light on that (I worked in a prion lab in 2006-07). Generally, disposable instruments and materials are used whenever possible and incinerated after use. Glassware is submerged in acidic detergent and autoclaved for 4 hours at (I believe) 132C. As far as I know, there is still no known way to completely sterilize stainless steel instruments - this was being studied at the time in the lab where I worked. Any piece of equipment that came in contact with human or bovine prions was kept in Biosafety Level 3 facilities permanently. I'm not sure what the decontamination process was for retired equipment. Separate equipment was maintained for "non-human pathogen" prions - hamster, mouse, etc.
