Catalysis of the reactions: inosine + O2 = 9-riburonosylhypoxanthine + 2 H2O; (1a) 2 inosine + O2 = 2 5'-dehydroinosine + 2 H2O, and (1b) 2 5'-dehydroinosine + O2 = 2 9-riburonosylhypoxanthine + 2 H2O.