On the 12th day of the Mahabharata war, Narakasura's son Bhagadatta, who was fighting on the Kaurava side, launched the Vaishnavastra or weapon of Vishnu at Arjuna, but Krishna covered Arjuna and absorbed the weapon with his chest. Arjuna asked Krishna why he would break his promise not to fight. Krishna responded that it's because the Vaishnavastra is an absolutely invincible weapon, capable even of slaying Indra and other gods, and can only be stopped by Vishnu, as described in this chapter of the Drona Parva of the Mahabharata:
Listen, O Partha, to this secret and ancient history as it is, O sinless one! I have four forms, eternally engaged as I am in protecting the worlds. Dividing my own Self, I ordain the good of the worlds. One form of mine, staying on the earth, is engaged in the practice of ascetic austerities. Another beholdeth the good and the evil deeds in the world. My third form, coming into the world of men, is engaged in action. My fourth form lieth down in sleep for a thousand years. The form of mine which awaketh from sleep at the end of a thousand years, granteth, upon awakening, excellent boons to persons deserving of them. The earth, knowing (on one occasion) that that time had come, asked of me a boon for (her son) Naraka. Hear, O Partha, what that boon was. Possessed of the Vaishnava weapon, let my son become incapable of being slain by the gods and the Asuras. It behoveth thee to grant me that weapon. Hearing this prayer, I then gave, in days of old, the supreme and infallible Vaishnava weapon to the Earth's son. I said also at that time these words, 'O Earth, let this weapon be infallible for the protection of Naraka. None will be able to slay him. Protected by this weapon, thy son will always, in all the worlds, be invincible and crush all hostile hosts.' Saying, So be it! the intelligent goddess went away, her wishes fulfilled. And Naraka also became invincible and always scorched his foes. It was from Naraka, O Partha, that the ruler of the Pragjyotishas got this weapon of mine. There is none, in all the world, O sire, including even Indra and Rudra, who is unslayable by this weapon. It was for thy sake, therefore, that I baffled it, violating my promise.
I'm interested in the part in bold. My question is, what are the four forms of Vishnu listed by Krishna?
Do they have any relation with Vishnu's four Vyuha forms Vasudeva, Sankarshana, Pradyumna, and Aniruddha described in the Pancharatra Agamas, whom I discuss here? The fourth form who sleeps for 1000 years sounds like a description of Vishnu's Vyuha form Aniruddha, who sleeps during the Mahapralaya and then wakes up and creates Brahma from his navel. (Although a Mahapralaya lasts for a hundred years of Brahma, not a thousand.) And the third form sounds like Vishnu's Vyuha form Vasudeva, insofar as he dwells in Shwetadvipa in Bhuloka and he engages in actions when the gods go to him seeking help. But I don't see any correlation with the remaining two Vyuha forms.
The first form who stays on the Earth engaging in Tapasya sounds like Vishnu's incarnation sage Narayana. And I'm not sure what the second form, who witnesses good and bad deeds, is. It could be Antaryami Vasudeva, who is present as the indweller in the hearts of all beings and thus observes their actions. In any case, are there any scriptures or works of Acharyas which shed light on who these four forms are?