Moksha or Salvation in Vedas and Vedanta

Question

Are there vedic ways to get mukti other than the vedantic ways ― Karma yoga, bhakti yoga, jñāna yoga, and raj yoga?

Answer 1

Summarized outline regarding the concept of mokṣa in all the six systems of orthodox philosphy, according to a study on the Yogasutras:

Mīmāṃsā Darśana
According to ancient Mīmāṃsā philosophers, heaven was the highest attainment (mokṣa) of human life. One can get all the pleasures and the highest bliss in the heaven. Heaven can be attained by the yāgas, like jyotiṣṭoma etc. as it is said in Vedic scriptures. In the later period, Mīmāṃsākas concept about mokṣa changed as they got impacted by other philosophies. Further Mīmāṃsā philosophy got divided into two sects-
1 - Sect of Kumārila Bhaṭṭa:—According to this sect, Mokṣa is the state where the contact between the soul and the universe breaks. [...]
2 - Sect of Prābhākara Mīmāṃsāka:—According to this sect, mokṣa is ‘performing the rituals described in the Vedic Scriptures throughout life. [...]

Nyāya Darśana
Nyāyadarśana uses the word apavarga (for mokṣa), which literally means fulfillment or completion. The other word, niḥśreyas also occurs as alternative to mokṣa, which means most excellent or supreme good. According to Maharṣi Gautama (Nyāyasūtra, I.I.22), Release is the absolute deliverance from pain. [...] Nyāya accepts apavarga as only cessation of sorrow, not as a gain of happiness. As bliss creates desire to attain it, which again would lead ātman to bondage. This view was however criticized by other darśanas since as per them, if the state of liberation is like a stone nobody would wish to attain such a mokṣa.

Sāṅkhya Darśana
The very first sūtra of Sāṅkhya Darśana describes the concept of mokṣa as the state of being permanently free from three types of pains is called as final attainment, i.e. kaivalya. [...] According to Sāṅkhya philosophy, the relief from these three types of pains is possible only in the state of kaivalya. According to Sāṅkhya philosophy, kaivalya can be attained through the discriminate knowledge of two realities of puruṣa and prakṛti.

Vaiśeṣika Darśana
Vaiśeṣika darśana has close resemblance to Nyāya darśana but still has some different point of view regarding concept of mokṣa. Vaiśeṣika darśana shares the same views about the state of liberation as that of Nyāya i.e. absolute annihilation of pain. The way to attain the liberation is however different according to Vaiśeṣika. [...] If the mind is concentrated on the soul, the senses will not work, as they are under the control of the mind and mind would remain calm and still in the knowledge of the ātma. A deeper practice of Yoga leads to a meditating mind on the ātma leading to ultimate attainment i.e. niḥśreyas.

Vedanta Darśana

1. Advaita-Vedānta:—According to Advaita Vedānta, the Mokṣa is not only the state where all the pains get ceased but also it is the state of ultimate bliss as the Brahman itself is of ānanda nature. After Mokṣa, the universe does not disappear, but the perspective gets changed.
   
2. Dvaita Vedānta:—According to Dvaita Vedānta, knowledge of five fundamental, eternal and real differences makes the person able to attain mokṣa–[...] These five differences are said to make up the universe. The universe is aptly called prapañca for this reason After this knowledge faith on the God arises, which takes soul results to mokṣa.
   
3. Dvaitādvaita Vedānta:—To attain deliverance, the jīva has to commence with a complete submission to the paramātman, or prapatti, whose six constituents are—[...] God’s grace extends itself to those who are possessed of these 6 constituents of prapatti, i.e., who are prapanna; and by that grace is generated bhakti consisting of special love for him, which ultimately ends in the realization of (sākṣātkāra) of the paramātman.
   
4. Śuddhādvaita Vedānta:—If one wants to obtain mokṣa and the bliss given by Kṛṣṇa, the only path to do so is bhakti. In the Kaliyuga, it is believed that the forms of bhakti mentioned in the scriptures are nearly impossible to practice, so the followers of Vallabhācārya recommend puṣṭibhakti -which is the end itself and not means to an end, giving mokṣa, joy and oneness with Kṛṣṇa.
   
5. Viśiṣṭādvaita Vedānta:—This philosophy accepts the bhakti [2] (worship, devotion to the God) as the only means of Mokṣa. In the bhakti, the devotee surrenders everything to the God become unenthusiastic about the rest all things. [...] After the attainment of mokṣa, God gives the place to a devotee for residing in the heaven.

Yoga Darśana
Yoga treats specifically of the dynamics of the process for the separation, and outlines practical techniques for the obtainment of release, or kaivalya. [...] Through repeated daily practice of 8 yogāṅgas, diminution and consequent disappearance of impurities, there arises the illumination of knowledge, which develops up to the stage of vivekakhyāti (the ultimate realization of the discrimination between puruṣa and prakṛti).

See the source link for more details and references to canonical literature.