Einar Hugo Olsen studied at the Kunstakademiet (the Academy of Fine Arts) under F. Vermehren, Otto Bache, and Frants Henningsen from 1894 - 1899. He later travelled to Italy, the Netherlands, Belgium, Germany, and Norway. Olsen painted portraits, figures, interiors, and exteriors, but he was primarily a landscape painter. His naturalistic landscape and city paintings demonstrate his ability to create a whole and a balance in the motif, despite the dominance of characteristic elements such as large trees or marked buildings.
In the 1940s, Olsen was a member of the Deer Park group, a group of painters who concentrated on painting motifs from Deer Park. The big, old trees found in Deer Park became a frequent subject in a number of Olsen's paintings. He exhibited at a number of locations, most notably with the Deer Park group for more than a decade.