Is there any scriptural support for the existence of completely non-physical realms? If so, is there a Sanskrit term for it? Sukshma Loka?
According to the Vedas and Upanishads people who do not attain moksha go to the lunar world.
Residing in that (region of the moon) till they have exhausted (the results of action)  they then return  again  the same way as they came (by the path that is being mentioned).  They come to Akasa, and from Akasa to air. Having become air, they become smoke. Having become smoke they become the white cloud.
Having become the white cloud, they become the (rain-bearing) cloud. Having become the cloud they fall as rain. Then they are born in this world as rice and barley, herbs and trees, sesamum plants and beans.  But the release from these is more difficult,  for whatever eats the food and sows the seed, they become like only.
Chandogya Upanishad 5.10.5–6
Swami Swahananda, the translator, makes the following points about these 2 shlokas:
 The soul who returns from the lunar world does not do so having exhausted the entire store of this past Karma, but only that part of it which led to the attainment of that region is used up there.
 When the results of action are exhausted the aqueuous body of the region of the moon takes the subtle form like Akasa and remains in the sky. From the sky it successively appears as air, smoke, white cloud and (rain-bearing) cloud and then falls down in the form of showers of rain.
 The word again shows that he has been through all these stages before.
 There is no definite rule that they must come back passing through exactly the same stages as they want. In fact there are differences in the ascending and descending paths. Here one particular path is being mentioned.
 That is, they remain attached to the corn, etc. While mentioning the descent of the displaced souls the text refers to them with a singular verb, but in the last instance a plural verb is used. This is justified as follows. In the first instance they are taken as a unity represented by cloud etc., in which they dwell indistinctly. In the second case, the souls with residual Karma are many.
 There is no certainty where the rain-water will fall and where the Jivas attached to them will go. Moreover, the food along with the Jivas must be eaten by a man capable of producing children, then only can they enter the mother’s womb. To be attached to corn, etc. itself is difficult. To be born as corn etc is for some the last stage of this birth, not an intermediate stage before becoming man etc. In the form of corn etc. they exhaust their Karma and then are born again in another form.
Note of caution: Jivas only get attached to various food products like rice and barley and are not themselves rice and barley or corn.
Later Hindu scriptures mention non-physical realms like heaven and paradise.
Said the God of Fire: Samadhi denotes a state of mind in which the consciousness, appearing in its spiritual aspect, remains calm and self-contained in itself like a pacified lake or sea and ceases to be operative in the physical and intellectual plains. A yogin, whose mind deeply absorbed in meditation, remains steady and un-flickering like the flame of a lamp kept in a windless chamber or receptacle, is said to have attained to the spiritual state of Samadhi. In this experience a yogin usually loses all his faculties of sense-perception. He hears not, sees not, smells not, feels not when not touched, thinks not, but is inert and inoperative as a log of wood and spiritually rests in the bosom of Supreme Brahma, steady and stationary like the un-flickering lamp light in a windless room.
Miraculous powers and celestial attributes spontaneously develop themselves in a yogin, absorbed in meditating upon the universal soul symbolized by the god Vishnu and thus unmistakably indicate his success in connection with his practice of yoga. The gods wait upon him with the offerings of articles which they themselves enjoy in heaven. The yogin sees, with unaided eyes, unbounded treasures lying concealed in the bowels of the earth and hears the music of celestial spheres swelling in eddies around his person. Kings and rich men seek his favours by the gift of enormous wealth. The Vedas, the books of scriptures and sciences, as well as poetry and celestial alchemy, reveal to him their respective secrets and voluntarily furnish him with all knowledge contained in them. He becomes a healer of malady and a skillful artisan without going through the necessary term of training. Beautiful virgins of paradise hail him with their overtures and unsolicited affections. But a true yogin discards all these as so many trifles and with such man alone the god Visnu is pleased.
Agni Purana 376.1-10