The 27-year-old double amputee, who was one of the biggest names in world athletics, was last month convicted of culpable homicide, the equivalent of manslaughter, for killing Steenkamp, his girlfriend, on Valentine's Day in 2013.
Pistorius, who said he shot Steenkamp, a law graduate and model, after mistaking her for an intruder, faces anything from a suspended sentence or community service to 15 years in jail.
"This has ruined our whole family. It has ruined Uncle Barry and Aunty June. Reeva was everything to them. They adored her," Kim Martin told the court, referring to Steenkamp's parents.
In her testimony on the third day of the sentencing hearing, Martin painted a picture of a loving and deeply caring daughter who supported her parents as they "battled financially".
During the testimony, Steenkamp's parents struggled to hold back tears, while Pistorius, dressed in a dark suit and tie, bowed his head and appeared to weep.
On Tuesday, the court heard from Pistorius' defence that he had been making monthly payments to the Steenkamps as a show of remorse. The family confirmed they received 6000 rand ($US544) a month from Pistorius from March 2013 to September 2014 as part of a confidential agreement, adding the money would be returned after the deal was made public.
Pistorius' defence has been fighting to keep the athlete out of jail, citing his disability, his contribution to promoting sport among the disabled and the grim conditions in South Africa's overcrowded and violent prisons.
On Monday, a social worker recommended Pistorius be sentenced to three years of house arrest and confined to his uncle's Pretoria mansion and serve up to 16 hours of community service a month, which state prosecutor Gerrie Nel described as "shockingly inappropriate".
The state dismissed statements from the defence's final witness, probation officer Annette Vergeer, who said prison would "break" Pistorius because of his disability and psychological problems.
"You have a view of what happens in prison and you don't verify that view," Nel said, adding Vergeer's assessment was made after visiting only one small prison two years ago.
Judge Thokozile Masipa, only the second black woman to rise to South Africa's bench, had said she wanted to conclude sentencing by Friday.
A non-custodial sentence would be likely to cause public anger, fuelling a perception among black South Africans that, 20 years after the end of apartheid, wealthy whites can still secure preferential justice.
