It's difficult to respond to this question without seeming to express a critique of Eliot's verse that is not entirely positive. However, since Eliot has held an iconic status in the literary and intellectual world for a century, negative criticism is essentially irrelevant. Those features of his verse that do not conform to "traditional" poetic standards are those very things, often, that make his poetry so important and meaningful and that have been so influential in the modernist movement as a whole.

"Preludes" would seem to be, of the three named works in your question, the most straightforward, with each poem setting a mood and revealing the thoughts of those stuck in a grim urban milieu. If there is fragmentation, it consists of the use of truncated lines such as

The grimy scraps
Of withered leaves about your feet

and

The showers beat
On broken blinds and chimney-pots.

But there is also an arbitrary quality to the imagery, in which a disconnect is apparent, as in

The morning comes to consciousness
Of faint stale smells of beer
From the sawdust-trampled street.

The "morning" is rather unusually personified as "coming to consciousness," but the disconnect, in my view, lies in the association of "smells of beer" with, specifically, the street. Not to be facetious, but one would think the smell, if it were really there, would be noticeable as one approached a beer house, not rising from the level of the street itself. The phrasing is typical of the free associations in modernist poetry and in stream-of-consciousness prose as well. In "Prufrock," the fragmentation of ideas is even more evident than in "Preludes":

In the room the women come and go
Talking of Michelangelo.

This has nothing to do, at least on first glance, with the ideas that come before or after it. The famous opening of the poem already shows a disconnect between thoughts, a deliberate one: a "patient etherized upon a table" has nothing inherently to do with an "evening, spread out against the sky." Of course, all similes and metaphors (like those of one of Eliot's major influences, Donne) are the bringing together of seemingly unlike ideas, but in this case the pairing is jarring and inappropriate by "traditional" poetic standards. Even the description of the "evening spread out against the sky" makes little sense literally. But Eliot is presenting a purposely dreamlike world, a shifting phantasmagoria of the state of Prufrock's disordered mind—and by extension, that of modern man. Idea follows upon idea without outward logic:

Do I dare
Disturb the universe?
In an minute there is time
For decisions and revisions which a minute will reverse.

The concept of monumentally disturbing the universe is juxtaposed with a prosaic question of making decisions which "a minute will reverse." And in the lines

And I have known the eyes already, known them all—
The eyes that fix you in a formulated phrase,

the images are not easily reconciled, for the reader might puzzle over how eyes can fix one in a "phrase," whether a "formulated" one or any other kind. These are seeming disconnects that create an overall mood of randomness. They are non sequiturs that give the impression of a mental state of anguish and confusion.

"The Hollow Men," as intensely pessimistic a poem as any Eliot wrote, is relatively straightforward in its movement from thought to thought and image to image, and it is probably one of the least difficult of his poems to interpret. Yet we still see a juxtaposition of words and phrases that lack the continuity that would make them more obviously understandable:

Those who have crossed
With direct eyes, to death's other kingdom
Remember us

Adjectives are often used by Eliot in unexpected ways, but here, though the meaning of "direct eyes" is fairly clear, it is still an eccentric choice of words. That very unexpectedness enhances the unsettling effect of the poem and its account of these hopeless hollow men who are a metaphor for man alone in a hostile universe. The short, choppy quality of the lines conveys that same fragmented sense we find in the other poems.

In summary, Eliot's intention is to jar the reader with seemingly arbitrary, fragmentary, and disconnected ideas. These enhance the unsettled, disturbing character of both the form and content of his poetry, expressive of a world from which the bottom has dropped out.