Both lived in the Woodstock RD
Only 3 deaths for that name in that RD
1878 aged 81 - 1797
1903 aged 59 - 1844
1906 aged 82 - 1824
The most relevant death
1878 aged 81 - 1797
was for one buried in Kidlington the register reads:
1878 Jan 4 GILES Martin 81 Woodstock Union WB
I have taken this as the one on the 1871 census in Kidlington
"Martin GILES 74 an Ag Lab from Kidlington was with his wife Rosa 71."
So although the widow of the other one, Magaret, was still in North Aston in 1861 and 1871 and she was buried there in 1874, her Martin does not appear in the parish burial register. He was a coal merchant in 1851 and in the trade directonary in 1852 and as pointed ot a boatman in 1856
So where did he die between 1856 and 1861, Margaret was a widow with her daughter and son in lawin 1861.
The stretch of the Oxford Canal between Banbury and Tackley forms the eastern boundary of North Aston parish. So if he was transporting coal by boat it may be worth considering places along the Oxford canal does the whole area fall into the Woodstock registration district?
The Daughter was born in Upper Heyford another plac on the canal!