What are main prescribed religious duties for the members of different orders of varnashrama system?

The brahmacārī lives in the āśrama of the spiritual master and personally assists the ācārya. Householders generally are entrusted with the performance of sacrifice and Deity worship and should provide maintenance for all living entities. The vānaprastha must clearly understand the difference between body and soul in order to maintain his status of renunciation, and he should also perform austerities. The sannyāsī should fully absorb his body, mind and words in self-realization. Having thus achieved equanimity of mind, he is the best well-wisher of all living entities. Loving devotional service unto Lord Kṛṣṇa is the ultimate goal of the entire varṇāśrama system. In any social or occupational division of human society one must be a devotee of the Supreme Personality of Godhead and worship Him alone.

Source: A.C. Bhaktivedanta Swami Prabhupada (2014 edition), “Srimad Bhagavatam”, Eleventh Canto, Chapter 18 – Text 42 and 44.