Mother of 11, Mary McLaughlin, 58 was found dead at her home in Partick, in Glasgow's west end, in October 1984.
Graham McGill, 59, denies murdering her and fastening a ligature around her neck with intent to rape on September 26 or 27 that year.
Giving evidence at Glasgow High Court on Tuesday, one of Ms McLaughlin's sons, Martin Cullen, said he would visit his mother weekly at her third-floor flat in Crathie Court, Laurel Street.
He told jurors he went to his mother's home on October 2 1984, with his ex-partner and his child.
Mr Cullen said: "We noticed that the hall light was on and there was a strange smell coming through the letterbox.
"She would never have the light on, never."
Asked by prosecutor Alex Prentice QC to describe the smell, he said: "The most horrible smell you will smell in your life."
"I knocked on the window and shouted through. I ended up kicking the door in.
"My partner went in and came out screaming. I went to the end of the hall and I could not go any further."
He said he then phoned an ambulance and the police arrived.
During Mr Cullen's evidence, McGill was in the dock wearing a light-blue, rain jacket.
He is also accused of stealing keys from Ms McLaughlin's flat.
Ms McLaughlin was last seen alive on the evening of September 26 drinking at west end pubs including the Hyndland Bar.
She left at about 10.45pm to go to a chip shop on Dumbarton Road.
A post-mortem examination carried out on October 2 found she died of ligature strangulation at least five days previously.
The court heard the level of alcohol in her blood indicated she was "grossly intoxicated" at the time of her death.
Ms McLaughlin was unemployed and had previously gone by surnames Cullen and Mullen.
McGill was arrested by officers in December 2019 and charged after police interview.
He also faces a separate charge of threatening to murder Suzanne Russell and children at a house in Motherwell, North Lanarkshire, between January 1 1985 and December 31 1988.