In the 1850 US Census, Eliza Oakman, born Ireland about 1819, is living in the City of Troy, NY with her sisters Ann Oakman and Margaret Oakman.
The 1855 Census shows Eliza, Ann and Margaret living with their parents Walter and Eliza Oakman, along with their brother Walter and sister Jane.
By 1860 we find Eliza working as a Wash Woman, still living in Troy, NY, with her parents Walter and Eliza Oakman and sister Jane Oakman.
In 1870 Eliza is Keeping House for her father and younger sister, as well as as nephew and niece. I’ve not been able to find Eliza in the 1880 Census – she may have married or died by this time.