There's really no universal answer, but it depends on the university regulations and on your willingness to listen to students for several hours.
To give a personal example, I've been running oral exams for about 20 years. My exams, which are for undergraduate students (2nd or 3rd year), typically consist of a written test (2-3 hours) plus an oral exam with a duration of about 30 min for the standard exam or 1 hour if the student prepares an optional part (e.g. the presentation of a scientific paper or a presentation on a lab work). If you fail the written test, you cannot take the oral exam. You can be failed also at the oral exam too.
For me, the critical factor is the distance between two exam sessions because, given the rules in my country, the students who failed in one session should be able to retake the exam in the next one. Typically, in my university, the distance between two exam sessions at the end of a course is of a couple of weeks.
So, in my case, the magic number is of about 100 students, 150 maximum. Of 100 students, typically about 70 students come to an exam session. Of these, about 50% fail the written test, which means that I remain with about 35 students for the oral exam. Assuming that 1/4 take the optional part, I need 9+26/2=22 hours for the oral exams, which can be done in one week, leaving some days for grading and for rescheduling students who can have unexpected issues (illness, other exams on the same day etc.).
The benefits of oral exams have been discussed at length in the answers to this question, and I really cannot overestimate their importance in learning. See also this related question.