Even though this is an old query, I would like to give the information that I got from the official NIOS website. It is mentioned there that the results of the On-Demand Examination (ODE) are declared during last week of every month for the exams which were conducted during the preceding month.
Further, you will require the mark sheet for admission to the UG course. Hence you should also be aware that for the purpose of the mark sheets, those who appear for the ODE between May till October will be considered under the April exam of that year whereas those appearing during November till April will be considered under the preceding October exam. Accordingly, keep these aspects in mind when choosing the flexibility of when to appear for the ODE NIOS exam so that it is compatible with the admission schedule for your UG courses. Otherwise, you may miss out on admission due to the inability to produce the mark sheet in time.
When you make a commitment, you create hope. When you keep a commitment you create trust! ~ John C. Maxwell