Akon Guode's three youngest children, 16-month-old Bol, and four-year-old twins Hanger and Madit died after she drove the car into Lake Gladman in Wyndham Vale on April 8, 2015.

Another daughter, six-year-old Aluel, was also in the car but survived.

Guode, 37, appeared in the Supreme Court on Monday and pleaded guilty to one count of infanticide, two counts of murder and one count of attempted murder.

Her guilty pleas follow pre-trial hearings during which sensational claims of witchcraft, drug abuse by a witness and threats to kill were aired.

The Melbourne Magistrates Court previously heard that Guode never physically recovered after giving birth to Bol, and suffered headaches and dizzy spells, for which she did not seek medical help.

A witness reported overhearing Guode say on the day of the tragedy that she would rather end her life and those of her children than see the children live with Guode's husband and his new wife.

In the days after the deaths, the witness said Guode told her she drove the car into the lake, but that the husband's other wife had used witchcraft on her.

The court heard the witness, who cannot be named, was abusing alcohol and the drugs ice and cannabis.

The witness said that in the days after the youngsters drowned, she asked Guode what happened at the lake.

"I asked 'Did you do it?'," the witness said.

"[Guode said] 'Yeah I did what I did.'"

During one hearing, as an emergency call recording of another witness who saw the car being driven into the lake was played, Goude fell to the floor and wailed until proceedings were halted.

Guode's lawyer Julian McMahon climbed into the dock with his client, kneeling beside her and holding her hand as she continued to wail violently for more than 10 minutes.

The emergency call was made by Alexandra Colston-Ing, a teacher who happened on the scene and described seeing a car with somebody in the front and "movement in the back" driven "full bolt" into a lake.

Members of the Sudanese community who were present in the courtroom also began to sob.

Guode, from South Sudan, arrived in Australia in 2008 a widow with three children. Here, she and Joseph Manyang​ had four children together.

Mr Manyang, the father of the three victims, had defended Guode as a "loving mother" and said he did not believe she would have killed their children intentionally.

Guode's daughter Akoi Chabiet​ told the court that Mr Manyang's wife had threatened to kill her mother after the twins were born, though she denied this.

The children's funerals were held at St Andrew's Church in Werribee.

Goude sat in the church's front pew, the children's father at her side, looking over the three small, white coffins.

The mourners were mostly from the South Sudanese community and sat singing the call-and-response songs of the family's Dinka culture, until they gave way for the church's bells.

One mourner, Makok Kuol took to the pulpit to deliver the eulogies for his cousins, who he called "three beautiful angels".

Guode was charged with the children's murders several weeks later.

Infanticide has a lower moral culpability than murder, and carries a five-year maximum sentence rather than life imprisonment.

It applies to women who kill their children while affected by a mental disorder related to giving birth to them.

The Morwell woman's criminal trial was due to start in two weeks after she had earlier indicated not guilty pleas to the charges.

Justice Mark Weinberg​ remanded Guode in custody until her next court appearance on January 31.