Whether to go to New Oriental to learn oral English depends on your needs. If you teach oral English with foreign students and discuss it in groups, all institutions are similar, and New Oriental will not be much better than other institutions, except for the price.
Personally, I feel that the oral ability of New Oriental is mainly in the classroom of middle school professors. For example, listening and speaking classes, advanced listening and so on. Will involve the pronunciation and intonation of spoken language. I've heard several different kinds. The teacher's pronunciation is very nice.
No matter what kind of oral class you choose, the New Oriental teacher will teach some pronunciation skills, use movie lines, English songs and even rap. The classroom atmosphere is very pleasant. If you follow the teacher's method and practice regularly after class, you will certainly gain something.
If you want to strengthen the practice of oral fluency, you can also take some individual oral courses for exams, such as TOEFL and IELTS, to learn and expand topics.