Stres was born on 15 December 1942 in Donačka Gora. He attended primary school (four years) in his home village, and finished lower secondary school (four years) in Rogaška Slatina. He continued his studies at the Interdiocese Preparatory Seminary in Zagreb, Croatia (Croatian: Interdijecezanska srednja škola za spremanje svećenika v Zagrebu), taking his leaving exam in 1962. He entered the Congregation of the Mission, more commonly known as the Vincentians or Lazarists, on 22 August 1960 in Belgrade, Serbia.
Stres’ education was then put on hold for two years because of mandatory military service in the Yugoslav National Army; he was stationed in Ohrid, Macedonia.
After completing his military service in 1963, Stres entered the Faculty of Theology, of the University of Ljubljana, where he completed three years of study. Then he was sent to the Faculty of Theology at the Catholic University of Paris, where he received a Licentiate of Sacred Theology in 1969. During this time, he made his perpetual profession on 28 March 1967 and was ordained a priest on 20 April 1968. He continued his studies at the institute’s Faculty of Philosophy and received a M.A. in philosophy in 1972.