Much of the information about Delia and her parents is found in the Massachusetts Vital Records past 1841 which are available at the Massachusetts Archives, and online at the New England Historical and Genealogical Society. Fortunately, I'm a member and can look it up.
Mary (Thornton) Wheelock, wife of Henry Wheelock, died 9 Jan 1861 of consumption. Her death record indicates she lived in Dudley at the time. Her father's first name is indecipherable, but his last name is Thornton. (Mass Archives vol 149 : pg 221).
I could not find a second marriage record for Henry.
Delia Jane Wheelock was born in Webster, 19 Jan 1872, daughter of Henry (born Mendon) and Cordelia (born Charlton). (Mass Archives 243:328).
Delia J. Wheelock, daughter of Henry and Delia married Felix Martin in Webster on 15 Apr 1895. (Mass Archives 453:534).
Cordelia Wheelock's death is recorded in Webster, 25 Jan 1880.She died of cancer at age 49y 6m 17d. Her birth place is given as Charlton, her parents identified as Lucinda and James MaCoach(???). (MA 321:444)
Her birth record in Charlton is in the Mass VRs to 1850. She is Cordelia McCach, daughter of James and Lucinda, born 8 July 1830. She is listed under the Lyon surname - I'm not quite sure why. This may be an error in the NEHGS database, or there may be some association with the Lyon family.