Mr Little deliberately drove his car off the wharf and into 30-metre-deep water in a murder-suicide bid on Monday morning.

The bodies of Mr Little and his sons Koda, 4, and nine-month-old Hunter were pulled from the Ford station wagon shortly after police divers recovered a rifle from car.

Autopsies of the three bodies found gunshot wounds, police said on Friday.

"As part of the comprehensive report being prepared for the Coroner, police can comment that autopsies have been completed and revealed that Mrs Little's two young children suffered gunshot wounds prior to entering the water, as did Mr Little prior to driving over the wharf," SA police said.

The investigation is ongoing and police say issues including domestic violence and mental health will form part of a report to the coroner.

The South Australian fishing town rallied around Melissa Little, the boys' mother and Mr Little's wife, in the days following their deaths.

"Damien was my childhood sweetheart who became my loving husband. He was also a father who loved his two children very much," Melissa Little said in a statement. 

"Damien I loved you so much you have left a huge hole in my heart, our memories I will cherish forever, You will not be forgotten," she said.

Ms Little said she hoped her husband would be remembered as a well-respected and valued member of their family and community. 

Remembering her "two precious boys", Ms Little said Koda had "the biggest heart, so loving and caring".

"He always loved a hug, had so much enthusiasm and was a willing helper," she said.

She described baby Hunter as "happy, content and smiling".

"His laughter was infectious and his cheeky little personality was just beginning to emerge.

"I will miss them and think about them each and everyday. Their futures were full of endless possibilities," her statement read.

Police released photos of the Little family on Tuesday.

Mr Little's family has now revealed the 34-year-old had suffered with mental health issues for the past three years.

"We had noticed a change," his mother Sue told Adelaide's The Advertiser.

"We tried to help him, we all did. But you can't help somebody who can't help himself."

Lincoln South Football Club president Brenton Dennis said the entire community's thoughts were with the boys' mother Melissa Little.

"Our hearts go out to Mel. I wouldn't want anyone to be in the position she's in at the moment," he told the ABC. "It's just tragic and our hearts are with them and they're in our thoughts and our prayers."

The end of the wharf on Tuesday became a makeshift memorial as family, friends and members of the community laid flowers and stuffed toys for the two boys.

"It's just numbed the whole community. I just ask everyone to give the families all their love and respect and space that they need at this time," Mr Dennis told the ABC.

"I also ask everyone that you think about how our lives are at the moment and just put ourselves in their position and let's all make a promise to never let this happen again."

South Australian Commissioner for Victims' Rights Michael O'Connell said the heart-wrenching incident had caused anguish for the family and friends.

"But also to many who find murder by a parent to be among the cruellest of tragedies," he said.

"As people seek to come to terms with what has happened, they should be careful not to victim-blame.

"We do not know the reasons Damien did what he appears to have done and speculating helps neither the family nor the people of Port Lincoln."

Port Lincoln Mayor Bruce Green said the past 24 hours had been the worst day of his working life.

"This has taken everyone by surprise. It's a dreadful thing," he said.

"People are really trying to understand how this tragic event could have occurred.

"Apart from supporting family and friends, the next thing we need is how do we deliver support in the community to ensure these things don't happen in the future."

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Fairfax Media with AAP