The Pandavas & Draupadi are not "stuck" on the Earth. They were not "ordinary" human embodied jivas to start with. All of them were partial incarnation of highly exalted deities, as I discuss in this answer.
As per Mahabharata, they entered heaven, and later-on everyone got merged back into the deities they issued from.
- Description of the Pandavas and Draupadi as seen by Yuddhiṣṭhira in the Indra's heaven.
Section 4, Svargarohanika Parva
Vaishampayana said, "King Yudhishthira, thus praised by the gods, the
Maruts and the Rishis, proceeded to that place where those foremost
ones of Kurus race were. He beheld Govinda endued with his
Brahma-form. It resembled that form of his which had been seen before
and which, therefore, helped the recognition. Blazing forth in that
form of his, he was adorned with celestial weapons, such as the
terrible discus and others in their respective embodied forms. He was
being adored by the heroic Phalguna (an epithet of Arjuna), who also was endued with a
blazing effulgence. The son of Kunti beheld the slayer of Madhu also
in his own form. Those two foremost of Beings, adored by all the gods,
beholding Yudhishthira, received him with proper honours.
"In another place, the delighter of the Kurus beheld Karna, that
foremost one among all wielders of weapons, resembling a dozen Suryas
in splendour. In another part he beheld Bhimasena of great puissance,
sitting in the midst of the Maruts, and endued with a blazing form. He
was sitting by the side of the God of Wind in his embodied form.
Indeed, he was then in a celestial form endued with great beauty, and
had attained to the highest success. In place belonging to the
Ashvinis, the delighter of the Kurus beheld Nakula and Sahadeva, each
blazing with his own effulgence.
"He also beheld the princess of Pancala, decked in garlands of
lotuses. Having attained to Heaven, she was sitting there, endued with
a form possessed of solar splendour. King Yudhishthira suddenly wished
to question her. Then the illustrious Indra, the chief of the gods,
spoke to him, This one is Shri herself. It was for your sake that she
took birth, as the daughter of Drupada, among human beings, issuing
not from any mothers womb, O Yudhishthira, endued with agreeable
perfume and capable of delighting the whole world. For your pleasure,
she was created by the wielder of the trident. She was born in the
race of Drupada and was enjoyed by you all. These five highly blessed
Gandharvas endued with the effulgence of fire, and possessed of great
energy, were, O king, the sons of Draupadi and yourself.
- In the next chapter, it's revealed all the people involved in the Mahabharat got merged back into their original deity, they issued from.
Section 5,, Book 18 - Svargarohanika Parva
Bhishma of mighty energy and great effulgence attained to the status of the Vasus. Eight Vasus, O chief of Bharatas race, are now seen.
Drona entered into Brihaspati, that foremost one of Angirasas
descendants. Hridikas son Kritavarma entered the Maruts. Pradyumna
entered Sanatkumara whence he had issued. Dhritarashtra obtained the
regions, so difficult of acquisition, that belong to the Lord of
treasures. The famous Gandhari obtained the same regions with her
husband Dhritarashtra. With his two wives, Pandu proceeded to the
abode of the great Indra. Both Virata and Drupada, the king
Dhrishtaketu, as also Nishatha, Akrura, Samva, Bhanukampa, and
Viduratha, and Bhurishrava and Sala and king Bhuri, and Kansa, and
Ugrasena, and Vasudeva, and Uttara, that foremost of men, with his
brother Sankhaall these foremost of persons entered the deities.
Somas son of great prowess, named Varcas of mighty energy, became
Abhimanyu, the son of Phalguna, that lion among men. Having fought,
agreeably to Kshatriya practices, with bravery such as none else had
ever been able to show, that mighty-armed and righteous-souled being
entered Soma. Slain on the field of battle, O foremost of men, Karna
entered Surya. Shakuni obtained absorption into Dvapara, and
Dhrishtadyumna into the deity of fire. The sons of Dhritarashtra were
all Rakshasas of fierce might. Sanctified by death caused by weapons,
those high-souled beings of prosperity all succeeded in attaining to
Heaven. Both Kshattri (an epithet of Vidura) and king Yudhishthira
entered into the god of Righteousness (Yamaraja) . The holy and
illustrious Ananta (who had taken birth as Balarama) proceeded to the
region below the Earth. Through the command of the Grandsire, he,
aided by his Yoga power, supported the Earth. Vasudeva was a portion
of that eternal god of gods called Narayana. Accordingly, he entered
English Translation by K.M. Ganguli
As regards performing the final funeral rites and annual sradhhas rituals for ancestors, it is safe to assume that the onus fell on Parikshit since he was the successor and descendant of the Kuru dynasty.
Also, Yuddhishthira reached the heaven with his own body.
Section 3, Book 17 - Mahaprasthanika Parva
Shakra said, ‘Thou shalt behold thy brothers in Heaven. They have
reached it before thee. Indeed, thou shalt see all of them there, with
Krishna. Do not yield to grief, O chief of the Bharatas. Having cast
off their human bodies they have gone there, O chief of Bharata’s
race. As regards thee, it is ordained that thou shalt go thither in
this very body of thine.
To conclude -
The Pandavas and Draupadi are not "stuck" on Earth, they reached heaven, and ultimately merged into their original deity source.
The final rites, and other death rituals must be performed by Parikshit, the sole eligible male descendant of the Kuru dynasty.