Hi Swampinstein,
Burials that I've found on my burial disc are
Hannah Elks of Radford aged 74yrs at St Peter's Church Radford on 20 June 1834
Mary Elks of Radford aged 48yrs at St Peters Church Radford on 20 July 1842
Sarah Elks of Henry Street Sneinton aged 59yrs at St Stephen's Church Sneinton on 13 Dec 1857, this is Joseph wife.
Have not found a Thomas Elks.
On 1851 census Sarah is a widow living on Henry St, with daughter Harriett Elks born 1826 and granddaughter Harriett Elks born 1848.
Harriet Elk daughter of Joseph and Sarah christened 4 Dec 1825 Lenton Church
Harriet married John Haysom St Stephens Church Sneinton on 4 Jan 1858,
Maybe the Elks name could also be spelt as Ellis or Else too.
Wendy