Could you suggest the best position and props to achieve most comfort while sleeping with torn meniscus?
It depends. There are 2 menisci in the knee, medial and lateral. Tears can be anterior (in the front) or posteriorly (in the back). The most common tear is medial and posterior. Sleeping with the knee partially propped up in flexion will work, but your knee will typically tell you what feels best. If it continues to interfere with sleep and activites of daily living, you shuld have it treated (arthroscopy).
Pillow support. Usually the best position is to have the affected knee supported on a pillow with the knee slightly flexed. Unfortunately, I have many patients that say nothing helps at all until the tear is fixed. Good luck!