How to read aloud a sentence like 'In the year 18.. they decided to move to Bricktown'

How to read aloud a sentence like 'In the year 18.. they decided to move to Bricktown'? Such sentences are common especially in Victorian literature.

My only option is 'eighteen and something' but I feel that it will not do when reading aloud formal texts, e.g. citations from legal documents included into some fiction books.

You would not say "In the year eighteen and something", since that would not conform to the standard way of reading years. We don't put an "and" except after "hundred". In standard English we normally would say either:

In the year eighteen something

or

In the year eighteen hundred and something.

You could use "something", "thus and such", "and such", "some", or any similar phrase. The choice really depends on the register of the work and the interpretation you wish to give it (which might be out of scope for this board). Just consider that "mumble mumble" is extremely informal and perhaps comic, and "thus and such" is more formal and perhaps stilted.

I suspect that, at the time that this device was commonplace, no one really anticipated that their work would be read aloud (much less the explosion of the audiobook format may decades later!)

When I read this kind of thing out loud to my family, I usually say "In the year eighteen[mumble mumble mumble]" but that's a humorous decision, not an informed one...