Living systems create order within by creating even more disorder in the outside world. One can create order locally by putting energy into the system. Disorder created includes heat given off by the organism and waste products produced. Notice how waste products such as Carbon Dioxide and Urea are small fragments of larger molecules such as carbohydrates and proteins.
Sunlight is the ultimate source of energy for life on Earth.
Note that oxidation can occur in the absence of Oxygen. Prokaryotes don't use oxygen for breakdown. But oxidation occurs nevertheless. Oxidations release energy, reductions require energy. Biochemical reactions are aided by enzymes.