The Hindu trinity is of Brahma, Vishnu and Shiva. They are respectively the creator, preserver and destroyer of the universe. They are also aligned as the transcendent Godhead, Shiva, the cosmic lord, Vishnu and the cosmic mind, Brahma. In this regard they are called Sat-Tat-Aum, the Being, the Thatness or immanence and the Word or holy spirit. This is much like the Christian trinity of God as the Father, Son and Holy Ghost. The trinity represents the Divine in its threefold nature and function. Each aspect of the trinity contains and includes the others.
Each God in the trinity has his consort. To Brahma is Saraswati, the Goddess of knowledge. For Vishnu is Lakshmi, the Goddess of love, beauty and delight. For Shiva is Kali (Parvati) , the Goddess of power, destruction and transformation. These are the three main forms of the Goddess, as Brahma, Vishnu and Shiva are the three main forms of the God. The three Goddesses are often worshipped in their own right as well as along with their spouses.
Father of the Matrix => Brahma (The initial Creator)
Oracle => Lord Shiva and Goddess Shakti (Shiv and Shakti are often regaded as male and female counterparts of the same divinity. The Oracle tries to "unbalance" the equation, something akin to destruction of universe for good, which is Shiva's job. Shakti or the mother Goddess stands for love, and nurturing and Oracle seems to love kids, and not to mention candies)
Most importantly,
NEO => Lord Vishnu, the divine preserver, the saviour, and the one who periodically incarnates himself to destroy evil forces (e.g.: Smith).
A certain Hindu mythological depiction portrays that while Vishnu is the divine saviour and re-incarnates himself to cleanse the world, he in a certain sense collaborates with Brahma for creation of a new cosmos every time it is destroyed (there is a depiction of Brhama positioned on a lotus that arises from Vishnu's navel. Every time Brahma utters a word, a cosmos gets created, which eventually grows, matures, and collapses); Neo does something similar - he collaborates with the Architect, to re-set the Matrix, and at the same time saves Zion. The Bhagvad-Gita states that those devotees who follow the path of "dharma", truth and sincere devotion, realize that the world is "maaya" (illusion) and come to Vishnu, attain liberation from recurrent life-and-death cycles. Interestingly, this is similar to the saving of Zionites by Neo, and freeing up of countless others by Neo and Co.