Once Rhodes Scholars enter Oxford, they typically stay for two years -- although they can apply for a third. The goal of most is to earn a Master of Philosophy Degree or a Master of Science degree. Either degree can be in any subject -- choosing a Master of Philosophy degree doesn't mean the student is only studying philosophy. Instead, a Master of Philosophy degree is one that's earned through graduate-level coursework and examinations. The Master of Science is earned through research and examination.
Oxford is very different from most American colleges and universities. For one, it's made up of 38 colleges. Each college has separate admissions. In fact, winning a Rhodes scholarship is no guarantee that a given college at Oxford University will accept you. Also, while most American schools use classroom discussions, at Oxford, much of the instruction is one-on-one, with students working with a tutor in a particular area. The tutor assigns readings and an essay on a particular topic, and the student and tutor meet to discuss the assignments. Finally, whereas at American schools, the same person teaches and gives tests, at Oxford, the tests are given by a university Board of Examiners, not the student's tutor. The result of this system is that the tutor and student work in partnership to prepare for exams.
Rhodes scholars are allowed to study any subject they choose, so as you can imagine, the courses that Rhodes Scholars have taken are extremely varied.