These three forms are also known as Pon-mangai (Sridevi), Nila-mangai (Bhudevi), and Pula-mangai (Nila Devi).
Pulam translates to the human senses. Nila Devi is described as the Goddess of the Senses and Bliss.
The Sita Upanishad mentions that these three forms as those of goddess Sita; Niladevi is associated with Tamas. Niladevi besides Tamasa, is associated with the sun, the moon and fire.
“Mahālakṣmī is the different-and-non-different form of the Lord of lords (Nārāyaṇa), consisting of material (acētana) and spiritual (cētana) potencies, and in both features She acts as the willing energy (icchā), creative energy (kriyā) and the internal (sākṣāt) potency. The willing potency is again divided into three, namely Śrī, Bhū and Nīlā.”
—The Sita Upanishad
The philosopher-saint Parasara Bhattar beautifully echoed the Alvars, describing Krishna as being completely "intoxicated by her beauty" (Neela thunga sthana giri thati suptham)
In the famous Tiruppavai (composed by the saint Andal), she describes Krishna as sleeping with his chest rested upon the soft shoulders of Nappinnai.
Bhū and Nīla are considered as shadows and servants of Mahālakṣmī, for which the authority is Ṡrī-raṅgarāja-stava (Pūrva 63) of Parāṡara Bhaṭṭar, the direct disciple of Rāmānuja.
Direct evidence of the Nīla-sūkta is found in the Taittirīya Kṛṣṇa Yajur-vēda (4.4.12), where a Viṣṇu-patnī (mentioned twice) is glorified as Ghṛtavatī and Payasvatī (the bestower of ghee and milk). This serves as an allusion to Her incarnation as Nīlā-devī in Vṛndāvana during Kṛṣṇa’s childhood among a cowherd family (more on this later).
Ramayana Balakanda 1.14.18 mentions that Vishnu has three wives (tasya bhāryāsu tisṛṣu):
tasya bhāryāsu tisṛṣu hrī-ṡrī-kīrty-upamāsu ca viṣṇō putratvam āgaccha kṛtvātmānaṃ catur-vidham
Hrī is the personification of Lord’s kṣamā, i.e., forbearance and patience to forgive our mistakes, so it is Bhūdevī.
Ṡrī is the personification of Lord’s dayā, i.e., compassion, so it is the wealth-bearing Ṡrīdēvī.
Nīlā or Kīrti is the personification of Lord’s saundarya and audārya, i.e., beauty and generosity, so it is the glory-giving (kīrti) Nīlādēvī.
Nīlā posses qualities similar to Rādhā:
The 15th century Malayalam work “Krishna Gatha” by Cherusseri Namboothiri, specifies the name of the gopi as Nila, in this episode from Bhagavatam 10.30.37–38
7) Nīlā (नीला).—A Gopikā. Śrī Kṛṣṇa was one day picnicking in Vṛndāvana with the Gopī women, and they were proud that he was mad after them. To dispel their pride Kṛṣṇa disappeared abruptly from their midst and sported with the woman called Nīlā. Then she also became proud that Kṛṣṇa loved her more than the others, and she asked him to carry her on his shoulders. He stood there ready stretching his neck to carry her. But, when she stood with her legs parted to mount on Kṛṣṇa’s neck and looked for him he was missing; he had already disappeared. The Gopikās ultimately shed their pride and then Kṛṣṇa appeared before them. (Ceruśśeri’s Malayālam Epic Kṛṣṇa Gāthā).
Srila Prabhupada relates this episode to Radharani in his commentary, even though I clarify that the original Bhagavatam does not mention Radha’s name or Nila’s name at all in this context.
Nila is an Attendant of Lakshmi along with Bhumi.
Bhūmi-Nīlā-di-saṁsevye svāmi-cittānuvartini
Literal Meaning: "She who is thoroughly served by Bhumi, Nila, and others, and who acts in perfect accordance with the mind of her Lord."
—Lakshmi Sahasranama Skanda Purana
The Mahabharata Tatparya Nirnaya 13.48 to 13.50 describes Krishna’s marriage to Niladevi.
Garuḍa Purana, a Sāttvika Purāṇa, mentions that Nīlā was reborn as Nagnajitī-Satyā, the daughter of King Nagnajit.
Though primarily a hymn dedicated to the Lord of Tirupati (Śrīnīvāsa) and His divine compassion personified (Dayā), the Dayā Śatakam frames Dayā as an alternate form of Lakṣmī (Śrī). It features a famous verse highlighting Nīlā's role in masking the faults of devotees before the Lord.
निशामयतु मां नीला यद्भोगपटलैर्ध्रुवम् । भावितं श्रीनिवासस्य भक्तदोषेष्वदर्शनम् ॥ ८॥
—Dayā Śatakam
The Meru Tantra, refers a goddess called “ Shyama “ accompanied by Vishnu, who is most likely Nila because of the similarity in the meaning of name.
vi̠ṣṭa̠mbhō di̠vōdha̠ruṇa̍ḥ pṛthi̠vyā a̠syēśyā̍nā̠ jaga̍tō̠ viṣṇu̍patnī ॥
"[She is] the prop/pillar that holds up the heavens and supports the earth, the ruler of this [creation], the mistress of the moving world, and the consort of Vishnu."
—Neela Sukta
dhru̠vā di̠śāṃ viṣṇu̍pa̠tnyaghō̍rā̠-'syēśā̍nā̠saha̍sō̠yā ma̠nōtā̎ ।
"She is the steadfast [deity] of the quarters [directions], the auspicious consort of Vishnu, the ruler of this [universe], and the inspiring mind of the mighty strength (or fierce energy)."
—Neela Sukta