Skjønberg started his career in the banking industry in Kragerø and Skien, but in his twenties he was discovered in the amateur theater by a dance teacher, who recommended him to Alma Fahlstrøm in 1913.

Fahlstrøm referred him to Sophie Reimers for training, as well as for singing lessons with Maja Flagstad.

He was then engaged with the National Theater from 1920 to 1924 before he went to Chat Noir to work under Victor Bernau, where he remained until 1929.

[5] Skjønberg participated in a number of recordings for NRK's Radio Theater, and among other things can be heard in the series about Dickie Dick Dickens and Ibsen pieces such as The League of Youth.

Among the best known are Fant (1937), the banned film To mistenkelige personer (1950), and Vi gifter oss (1951).