Hi again James,
I understand what you are saying BUT things not feeling right is sometimes a poor substitute for facts

Anyway, one part of my hypothesis (and it was only one of many possibilities!) is now shown to be what actually happened i.e. both Benjamin & Caroline had passed away before 1891.
Something we don't know is whether Clara was still alive or was still around by that stage (unless she was the informant of their deaths - have you checked this out?).
Sarah could have been left in the care of her grandparents by Clara (for whatever reason) and could then have had nowhere to go when they died.
As for Elijah, he's not been found in any census either before or after his marriage (as far as I'm aware) so he could be anywhere and could be hiding under any name.
I'm being devil's advocate here but I'd still be following up on the workhouse/poor law records if only in order to rule out Orphan Sarah BROOKS conclusively.
Given that the idea of the workhouse/poor laws doesn't ring true to you (AND if you find that there are no poor law records!) then another possibility is that Sarah was living with the OAKLEYs in 1891 as a private arrangement (perhaps just a temporary arrangement) because the HOMER (and/or BROOKS) relatives simply didn't have room for her in their own accommodation.
We know nothing about the BROOKS family so, at this stage, can only explore the HOMER family.
Were any of Clara's siblings found in the 1881, 1891, 1901, and 1911 censuses? What were their situations?
In the censuses, I've noticed the following siblings but don't know if there were others and/or which if any survived and/or if they married:
*James b ca 1840 (in 1841 and 1851)
*Mary Anne/Maryan b ca 1841 (in 1851 and 1861)
*Sarah b ca 1850 (in 1851 and 1861)
*Benjamin b ca 1853 (in 1861 and 1871)
*Matilda/Tilda b ca 1856 (in 1861 and 1871)
*Clara b ca 1859 (in 1861 and 1871 - and then, after her marriage, in 1881)
Perhaps you could tell us which of her siblings survived and the married named of sisters and any census references after any siblings had left home?
Sorry for all the questions but I, and obviously others, really would like to help
As you haven't managed to find Elijah before or after his 1878 marriage cert (unless he was the informant on Sarah Sophia's birth certificate - have you checked this out?), as you haven't managed to find Clara after 1881, and as you haven't managed to find Sarah in 1891, you probably do need to consider every possibility however unlikely it might seem.
Very best of luck,
JAP
PS: AMBLY and Spidermonkey, do you have any other ideas? Finding the Eli BROOKS/Clara SPRUCE marriage in 1880, and the SPRUCE lodger in the 1891, for the other Eli BROOKS was brilliant! Though, as Spidermonkey suggested, perhaps Elijah had a double life! Perhaps he was running two households and had a penchant for ladies called Clara

. And Mr Grinch did say that Elijah was a puddler on the marriage cert to Clara HOMER (Mr G, you said he was a labourer on Sarah's marriage cert; what was he on her birth cert?). But that probably means little as puddler was surely a very common occupation in the area ...