Dear Annette,
Gosh what a lot of effort you have gone to, I am really grateful, another pair of eyes often sees things...
I'm trying to absorb it all:
I do have a birth for Eliza in 1854 - from GRO -
HANSON, ELIZA mmn BENSON
GRO Reference: 1854 J Quarter in OXFORD Volume 03A Page 535
and, as you say, in 1871 she is living with her sister Emma in Sandiacre and in 1861, aged 7, she is living with her widowed aunt Elizabeth Walsham in Leeds.
She is actually the 10th child born to Thomas Hanson and Eliza nee Benson. Her parents are, as you say, Leeds born, but in 1851 they are living in Summertown, Oxford, which tallies with Eliza's birth there in 1854.
My guess at the moment is that her mother died after she was born, and before the 1861 census, and hence Eliza was staying with her aunts as she grew up. I cannot find any likely ref in the 1881 census for her.
Her father Thomas was named on her siblings marriage certs - 1862 & 1865 - but not as deceased, but I cannot (yet) find him in 1861.
I have found a death and burial for an Eliza Hanson, in Leeds, Hunslet Cemetery on 5 Apr 1885 which looks a possibility. I will need to see the death cert to se if there is anything else useful on it.
All for now, and thanks again,
Pam