Little is known of Morets life until he began his military service in 1875. Jules La Villette, his commander in Lorient, who first noticed his artistic talents, introduced him to Ernest Corroller, a drawing teacher and marine painter. Corroller taught him the art of landscape painting as practiced by masters such as Corot and Courbet, enabling him to register at the École des Beaux-Arts in Paris where in 1876 he studied under Rudolf Lehmann, Jean-Léon Gérôme and later, from about 1880, under the history painter Jean-Paul Laurens at the Académie Julian.
Olrik also specialized in still lifes, landscapes, historic, and religious paintings. Some of his religious works can be found in Marble Church and St. Mathews Church in Copenhagen.