www.freebmd.org.uk shows their marriage in the June quarter 1871 in Woodbridge Suffolk registration district vol 4a page 957. If you purchase the marriage cert from the GRO at http://www.gro.gov.uk/gro/content/certificates/http://www.gro.gov.uk/gro/content/certificates/ you'll learn fathers' names.
You can search the 1881 census, and others, free at www.familysearch.org where, living at Kirton, William was 36 born Bucklesham, Elizabeth 34 b Burstable, and three children George 9, Nelly 6 and Willie 2 all b Kirton.
In 1871 Elizabeth Hood 22 unmarried b Burstall was a visitor in Bucklesham in the household of John and Charlotte Stollery which included William unmarried age 26.
In 1861 she was a 12 year old servant born Burstall in Willisham Suffolk in the household of William Aldous, 27 beer house proprietor.
And finally in 1851 she was living with her parents in Burstall William Hood head marr 29 ag lab b Sproughton Suffolk Caroline Hood wife 24 b Burstall George Hood son 6 b Burstall Elizabeth Hood dau 2 b Burstall
The IGI at www.familysearch.org shows her baptism at Burstall on 16 Jul 1848, the daughter of William and Caroline. The IGI also shows a marriage at Burstall on 11 Aug 1844 between William Hood and Caroline Woodward
All of the above came from the free sites mentioned