The family had often played together, using their combined initials to call themselves Trio Lenajo.
Ms Strelchenko, who was also known as Natalia Strelle, was born in Russia but spent much of her life in her husband's native Norway. Her family said in a statement: "Natalia was a talented, beautiful, much loved mother, daughter, sister and friend. She will be greatly missed."
A post mortem examination found that she died as a result of multiple head and neck injuries.
Ms Strelchenko performed her first concert aged just 12 with the St Petersburg Symphony Orchestra.
She went on to play at some of the world's most revered concert halls, including Wigmore Hall in London, Carnegie Hall in New York and the Franzosische Dom in Berlin.
This year, she had already performed 17 concerts worldwide and was next due to perform a Mozart Concerto with the Minsk Chamber Orchestra in Oslo.
Neighbours said the family were not often at home because they were regularly on tour. They were often abroad with Leo as he entered international competitions.
Claire Parmley, 35, said: "I heard her screaming in the early hours of the morning so went outside to see what was going on. It must have been pretty loud because we heard it from down the road."
Det Supt Phil Reade, from Greater Manchester Police, said: "This is a tragic incident in which a talented young lady has lost her life.
"We have a team of detectives investigating this murder and are asking for anyone with information that may assist our inquiries to please get in touch."