I wrote an answer based on my personal experiences, but here is another based entirely on the literature.
From , well-designed oral exams can increase student success:
Scores on the oral examinations in advanced inorganic chemistry are usually about 15–20% higher compared to scores on written examinations over similar material. All students who performed at an unsatisfactory level on the first quiz in the introductory course earned a satisfactory mark after taking the oral quiz. Four probable reasons explain the higher scores:
The most significant contributor to higher grades is the self-correcting nature of the oral format—students always arrive at a correct response before moving on to the next question. This correct response, even though they might have been assisted to reach it, sets the stage for them to answer subsequent questions correctly. On traditional written examinations, missing the first part of a multipart question often results in answering all parts of the question incorrectly.
Requiring students to think aloud during the oral examination makes them think more carefully. This extra measure of care is often evident as a student will start a response, and then, even before they have completed their initial thought, will see a better way to look at the problem and logically work their way to a correct answer from a new starting point.
The oral examination tests a relatively small body of material and students are able to focus their study efforts. This focus is surely intensified by the knowledge that the testing will be done one-on-one. They do not want to do poorly in such a personal situation.
When testing some concepts, such as crystal packing or molarity, the questions are concrete in that students have objects to manipulate.
and this is especially true of weaker students:
Struggling students, in particular, appear to benefit from the oral examination format. The success of these students seems largely to derive from the increase in motivation as a result of personalized strategy instruction, an important component of the ICML. Personalized strategy instruction leads to improved performance and the satisfaction of doing well increases their desire to continue doing well. Many of these weaker students fear college-level chemistry before entering the course. Doing poorly on the first quiz confirms the view they hold of themselves as learners of scientific material. The personal, early intervention that oral quizzes provide enables them to perform better the rest of the semester.
Also, students think that oral exams do a better job of assessing what they know:
Student comments about the oral examinations obtained in anonymous course evaluations and personal exit interviews at the end of the term have always been consistent and enlightening. Most students believe that the oral examination provided a fair reflection of their knowledge. They were satisfied with their performance and would welcome oral examinations in other classes. Most students reported studying more for the oral examinations. Surprisingly, about half of the students interviewed volunteered that the oral examination provided a better reflection of their knowledge compared to written examinations because on written exams they could write something that was “fairly close” to being correct and get by with it. These students thought that the oral exam format made them demonstrate their understanding of the material.
For further reading, here's a small reference list:
 Roecker, L., 2007. Using Oral Examination as a technique to assess student understanding and teaching effectiveness. J. Chem. Educ, 84(10), p.1663.
 Luckie, D.B., Rivkin, A.M., Aubry, J.R., Marengo, B.J., Creech, L.R. and Sweeder, R.D., 2013. Verbal Final Exam in Introductory Biology Yields Gains in Student Content Knowledge and Longitudinal Performance. CBE-Life Sciences Education, 12(3), pp.515-529.
 Dicks, A.P., Lautens, M., Koroluk, K.J. and Skonieczny, S., 2012. Undergraduate oral examinations in a university organic chemistry curriculum. Journal of Chemical Education, 89(12), pp.1506-1510.
 Marino, R., Clarkson, S., Mills, P.A., Sweeney, W.V. and DeMeo, S., 2000. Using poster sessions as an alternative to written examination—the poster exam. J. Chem. Educ, 77(9), p.1158.
 Pearce, G. and Lee, G., 2009. Viva voce (oral examination) as an assessment method insights from marketing students. Journal of Marketing Education, 31(2), pp.120-130.
 Sayre, E.C., 2014. Oral exams as a tool for teaching and assessment. Teaching Science, 60(2), p.29.
Benefits to Oral Examinations
Allows direct, dialogic feedback: Oral exams provide instructors with an excellent opportunity to immediately diagnose and correct any major misconceptions. The face to face dialogue, through which this occurs, as well as the high-level, holistic nature of well written oral questions, creates an intense experience conducive to breakthroughs in student understanding of material. For this reason, oral exams are well suited for final exams, giving instructors one last chance to greatly affect student knowledge.
Encourages in-depth preparation: The unique anxiety associated with both public speaking and testing can provide a powerful impetus for student preparation, especially because good oral examination questions will center on synthesis and overall evaluation of material.
Demands different skills: Students are tested frequently, yet those tests are almost exclusively either written essay exams or standardized tests. Rarely do those students more skilled at making an oral argument than a written one get a chance to display their mastery of course content in the format where they display the most acumen.
Valuable practice for future professional activity: Whether they apply to graduate schools or try the job market, most students will find their futures heavily influenced by brief, stress-filled oral interviews for which they have received little preparation. Oral exams can help students to develop the necessary ability to remain collected while cogently answering difficult questions.
Reduced grading stress:Oral examinations can require severe schedule juggling and the sacrifice of some additional time by the instructor so that each student has an available time to take the test. However, as long as time is taken beforehand to carefully choose grading criteria and design a rubric, these exams offer many of the advantages associated with essay exams, such as developing skill in organization, synthesis, evaluation, and critical thinking, with much less grading hassle.