The Sanskrit philosophical school called Vaiśeṣika is the one most directly dealing with ontology. Its fundamental text is the Vaiśeṣikasūtra, which is commented upon by Prāśastapada in the Pādarthadharmasaṅgraha (from now one PDhS) (the following is a summary of Padārthadharmasaṅgraha ad 8.7).

The school distinguishes substances and qualities. The first group includes four types of atoms (earth, water, fire, air) and then aether, time, space, ātmans and internal organs (manas). The latter are needed as a separate category, because they are point-sized and therefore not made of atoms, unlike the external sense faculties.
Among the 17 qualities, it recognises parimāṇa or `dimension’. This encompasses at first two possibilities, namely atomic (aṇu), or extended (mahat). The former covers partless entities that have allegedly no spatial dimension, like points in Euclidean geometry and atoms themselves. These are considered to be without extension and permanent through time (nitya). The latter is subdivided into mahat and paramahat. The first covers all objects one encounters in normal life, from triads of atoms (imagined to be of the size of a particle of dust, the first level of atomic structure to be extended) to the biggest mountain. These entities have parts and extension and have an origin and an end in time. The second subdivision covers special substances, listed as ākāśa `aether’, space, time and ātmans, which need to be imagined to be present at each location. Such entities are also imagined to be nitya, that is permanent through time. In other words, they are present at each location of time and space.
The above also implies that entities considered to be permanent through time can only be either atomic or all-pervasive.

However, space, time, aether and selves (ātman) are present at all locations in different ways.

About aether, to begin with, texts like Jayanta’s Nyāyamañjarī say that it needs to be accepted as a fifth substance in order to justify the diffusion of sound across multiple media. Texts of the Vaiśeṣika school, and of the allied school of Nyāya specify that aether does not occupy all locations, but rather is in contact with each individual atom):

[The aether’s] all-pervasiveness consists in the fact that it is in contact with each corporal (mūrta) substance.
(sarvamūrtadravyasaṃyogitvam vibhutvam (Tarkasaṃgrahadīpikā ad 14).)

This means that aether does not pervade atoms, but is in contact (saṃyoga) with each one of them.

This point is already explicit in the allied school of Nyāya, the Nyāyabhāṣya, and is needed because of the point-sized nature of atoms. If these were pervaded by aether, then they would have parts, and thus not be permanent. These undesired consequences are examined in the following:

This is impossible, because of the penetration through aether || NS 4.2.18 ||

It is impossible for an atom [to be] partless and permanent. Why? Because of the penetration through ether, that is, because an atom, if it were permeated, that is `penetrated’ by aether, within and outside, then, because of this penetration it would have parts, and due to having parts it would be impermanent.

Or, the aether is not all-located} || 4.2.19 ||

Alternatively, we don’t accept that. There is no aether within the atoms and therefore aether ends up not being all-located

(ākāśavyatibhedāt tadanupapattiḥ || 4.2.18 ||
tasyāṇor niravayasya nityasyānupapattiḥ. kasmāt. ākāśavyatibhedāt. antarbahiścāṇur ākāśena samāviṣṭo vyatibhinno vyatibhedāt sāvayavaḥ sāvayavatvād anitya iti.
ākāśāsarvagatatvaṃ vā || 4.2.19 ||
athaitan neṣyate paramāṇor antar nāsty ākāśam ity asarvagatatvaṃ prasajyeta iti.)

Aether is postulated as a substrate of sound (which can move through solids, liquids and air, thus proving that it has neither earth, nor water, nor air as substrate). Thus, it needs to be unitary (multiple aethers would not explain the propagation of sound, sound would stop at the end of the respective aether) and it needs to be present at all locations (for the same reason). More in detail: Only because of the unitary nature of aether is it possible for sound to travel between different loci. Otherwise, one would have to posit some mechanism to explain how the sound encountered in one aether travels to another one. Instead, the simpler solution is to posit that aether is necessarily both single (eka) and present at all locations (vibhu).

As for ātman, the self is by definition permanent (otherwise, no afterlife nor cycle of rebirths would be possible). It cannot be atomic, though, because the ātman is the principle of awareness and people become aware of things potentially everywhere. The fact that they don’t become perceptually aware of things being, e.g., behind a wall, by contrast, is only due to the fact that the ātman needs to be in touch (via the internal sense organ, manas, which is believed to be atomic and to move quickly from one to the other sense-faculty) to the sense faculties (indriya) in order for perceptual awareness to take place. Yogins are able to perceive things their bodies are not in contact with because their ātmans are omnipresent, like our ātman, and are able, unlike our ātman, to connect with other bodies’ sense faculties.
Within Sanskrit philosophy, Jaina philosophers suggested that the ātman is co-extensive with the body, since it can experience whatever the body can experience. Vaiśeṣika and other non-Jaina authors disagree, because this would lead to the absurd consequence of an ātman changing in size through one’s life.

A further element to be taken into account with regard to theories of location, and in particular while adjudicating whether they are about occupation or non-occupation is materiality.
Occupation of space seems to occur only from the level of atomic triads up to big, but not all-located, objects. Atoms are said to be mūrta and mūrta is usually translated as `material’, but taken in isolations, atom do not have parts and are only point-sized. In this sense, their being mūrta refers more about their being fundamental for material entities, rather than being material if taken in isolation. The distinction is theoretically relevant, but less evident at the pragmatic level, given that atoms are never found in isolation. Being mūrta is attributed to atoms of the four elements (not to aether) as well as to the inner sense organ (Nyāyakośa, s.v.), but not to ātman neither to aether.