Together with his classmates in the summer of 1941, he was sent as a cadet to the 2nd Kharkiv Tank School. After graduating from the school in 1942, he received the rank of lieutenant and was sent to the Gorky Automobile Plant, which then began to produce tanks. Member of the CPSU (b) since 1942.
The platoon commanded by O. Liashko received combat vehicles and was transferred to the North Caucasus Front. After a well-organized repair of military equipment in 1943, he returned to the tank school, where he taught special subjects until the end of the war.
From 1945 he worked as an engineer on the equipment of the open-hearth shop at the Novokramatorsk Machine-Building Plant of the Stalin Region. At the same time, he studied at the Donetsk Industrial Institute, graduating in 1947 with a degree in metallurgical and mechanical engineering.
From 1947 he was deputy head of the transport department, deputy director, and from 1951 he was a party member of the Central Committee of the CPSU (b) at the New Kramatorsk Machinebuilding Factory in Stalino Oblast.
From August 1952 to 1954 he was the first secretary of the Kramatorsk city committee of the Communist Party of Stalino Oblast.
From 1954 to 1957 he was secretary of the Stalino Oblast committee of the Communist Party. From 1957 to 1 March 1960, he was the second secretary of the Stalinist regional committee of the Communist Party.
1 March 1960 — January 1963 he First Secretary of the Stalino Oblast Committee of the Communist Party. In January — 11 July 1963 — First Secretary of the Donetsk Regional Industrial Committee of the Communist Party.
2 July 1963 — 18 March 1966 — Secretary of the Central Committee of the Communist Party of Ukraine, Chairman of the Bureau of the Central Committee of the Communist Party for Industry and Construction.
18 March 1966 — 19 June 1969 — 2nd Secretary of the Central Committee of the Communist Party.
On 9 June 1972, Liashko became Chairman of the Council of Ministers of the Ukrainian SSR. In May 1986, he headed the Republican Government Commission for the Elimination of the Consequences of the Chernobyl Accident. On 10 July 1987, the fifth session of the Verkhovna Rada of the Ukrainian SSR relieved Liashko of his duties as Chairman of the Council of Ministers of the Ukrainian SSR.
Since 1987 he has been a personal pensioner of union significance in Kyiv.
He was married to Davydova Klavdia Andriivna, and had two children, Volodymyr and Nina.
Author of three books of memoirs: "The Way of Survival", "The Way to the Nomenclature" (1997), "On the Steps of Power" (2001).
He died on 9 October 2002. He was buried in Kyiv at the Baikove Cemetery.