According to this site, liquid oxygen has proven to be effective in treating genital herpes and certain cancers. Liquid air is obtained by the rapid expansion of high pressure gaseous air which has been purified to remove CO2, and other high boiling substances, e.g. hydrocarbons, that might plug the expansion orifice. The liquefaction occurs because of the Joule-Thomson effect. You can find this discussed in detail in any physical chemistry or thermodynamics text. Liquid oxygen boils at -183 C., so ingestion would produce severe cryogenic burns, which I put in the category of seriously harmful side effects.
Liquid oxygen is a powerful oxidizing agent.
It reacts explosively with any organic substance, and even metals. For example, steel wool. I do not believe it would be used in any medical application involving direct contact with tissue. Liquid nitrogen, which boils at -196 C. on the other hand is chemically inert and is very commonly used by physicians to remove warts and other skin lesions. Argonne National Laboratory, Division of Educational Programs, Harold Myron, Ph.D., Division Director.