Agnihotra

H.H. Sri Swami Sivananda:

The Pitris remain in heaven, Pitri Loka or Chandra Loka, for a very long period. The enjoyments in heaven and the peace of the departed soul are enhanced by the performance of the Shraddha ceremony. Likewise the sufferings of the departed soul in worlds other than heaven are mitigated by the performance of the Shraddha ceremony by his sons. Thus, in both cases, the performance of Shraddha is a great help.
And even if the individual takes another birth immediately after his death, as happens in rare cases, the performance of Shraddha adds to his happiness in his new birth. So, it is the imperative duty of everybody to perform the Shraddha ceremony for his parents and forefathers. The Shraddha ceremony should be performed with great Shraddha or faith as long as you live. Faith is the main support for religion.
The various religious observances imposed upon mankind by the Shastras tend to purify the ignorant man. The Shraddha ceremony, being one of the obligatory duties as per the injunctions of the scriptures, also tends to purify the mind. Besides this, the forefathers are also pleased and their good wishes and blessings tend to our material and spiritual growth.

H.H.Sri Swami Sivananda:

Realized souls, who wish to help the devotees even after they give up their physical bodies, retain their astral bodies (Sukshma Sarira) for the sake of their eagerness to help those that are in need of their help. But Jivanmuktas, generally, do not retain their astral bodies just in order to help the aspirants, since there will always be highly evolved souls on the relative plane, who will carry on the task of teaching the spiritual aspirants.