I wrote an answer based on my personal experiences, but here is another based entirely on the literature.
From [1], 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:
[1] Roecker, L., 2007. Using Oral Examination as a technique to assess student understanding and teaching effectiveness. J. Chem. Educ, 84(10), p.1663.
[2] 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.
[3] 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.
[4] 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.
[5] 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.
[6] Sayre, E.C., 2014. Oral exams as a tool for teaching and assessment. Teaching Science, 60(2), p.29.