Kriukow was born on January 19, 1895, in the town of Orgeev, in Bessarabia, where his father, an official of the Russian Empire, worked at the local court of justice.

As a young man he studied at Fedir Krychevsky's art school in Kiev, and after finishing his training in 1918 he moved to Kamenets to teach at the local tekhnikum.

From 1944 to 1948 he lived in Austria, and painted under the pseudonym of Ivan Usatenko, taking part in art exhibitions in Salzburg, Innsbruck, etc.

In 1948, he emigrated to Argentina with his wife, fellow Ukrainian artist Olga Gurski, and settled in Buenos Aires, where he held personal exhibitions in the most renowned art galleries, such as Müller, Van Riel, and Whitcomb, almost yearly (1949–1965).

After his death in 1967, the well known Ukrainian writer and poet Igor Kaczurowskyj (the painter's son in law) was inspired by some twenty pictures Kriukow had made, in his spare time, on the subject of the old Ukrainian tale about the cat "Mister Kotsky", to write a long poem for children, which, many years later (1992) was to be published in Ukraine, illustrated by these same pictures from the artist's heritage.

In 1965, he was invited to exhibit in Buenos Aires Town Hall, after having received two important rewards: 1964, for his drawing Don Quixote, presented at an international art competition of the "Codex" publishing house, Madrid, and for his drawing Don Segundo Sombra, from "Codex Argentina".

He is the author of a large oil picture of Cardinal Josyf Slipy, and of the Argentine heroes José de San Martín (at the battle of Chacabuco; Buenos Aires Town Hall), and Admiral Guillermo Brown (unfinished; donated by his family to the Brown Institute after his death.

His last, finished, work was the apsis mosaic of The Virgin and Child, executed for the Ukrainian cathedral of the ''Holy Protection'' in Buenos Aires, and crowned by Pope John Paul II, in 1988, the millennium of Christianity in Ukraine.