The medical tests is an obvious requirement for admission at IIT Bhubaneswar as given in annexure IV. If by chance, you couldn’t get that done then you can get it from the institutes linked with the hospitals taking these tests.
IIT Bhubaneswar asks about your medical report before you are going for the counselling in a prescribed manner. It is not a hectic process and should not be much of a hassle. It's better that you complete the tests in your home and thus it makes the registration process easier.
You have to take the printout of the form provided by the IIT and visit the nearest government hospital. You will be provided all the reports within 3 or 4 days after the medical reports come. Even some of the government hospitals give the reports the next day, so there is no need to get worried.