At around 2.30pm on Tuesday, the 63-year-old woman was watching tv in her home on Delph Lane, Delph, when the men opened the back door of her house.
They claimed they were police officers and were checking houses to make sure they were okay. They searched the house and when the victim realised they were taking personal property, she tried to intervene and was knocked over.
All four men then left, taking jewellery, a Territorial Army medal, wedding rings and a gold St Christopher chain and pendant.
One man is described as being dark skinned, clean shaven, dark eyes, 5ft 8in tall, thin faced, wore dark clothing, black leather style cap, spoke English but addressed the other men in an unknown language.
Another male was dark skinned, 5ft 8in tall, had dark greasy hair that was combed across to the side, dark eyes and of thin build.
A third man was white, 6ft tall, in his early 20s, of broad build, had chubby cheeks, blue eyes, wore light blue jeans and a light grey puffer jacket.
Detective Constable Kelly Bragg said: “The woman is understandably distressed by what happened, these men walked into her home uninvited and she was completely powerless to stop them from stealing her personal property.
“I would ask anyone who may have information as to who these males are or where her possessions are to contact us. The items are not worth much in monetary value but to the victim, they are priceless mementos of her life.
“It is also essential to remind people to always ensure all of their doors and windows are locked at all times, even if you are in the house at the time. In addition, please do not let anyone into your house whose identity you are unsure of.”
Anyone with information should phone police on 0161 856 8850 or the independent charity Crimestoppers, anonymously, on 0800 555 111.