Given a set F of oriented graphs, a graph G is a Forb_e(F)-graph if it admits an F-free orientation. Skrien showed that proper-circular arc graphs, nested interval graphs and comparability graphs, correspond to Forb_e(F)-graph classes for some set F of orientations of P₃. Building on these results, we exhibit the list of all Forb_e(F)-graph classes when F is a set of oriented graphs on three vertices. Structural characterizations for these classes are provided, except for the so-called perfectly-orientable graphs and the transitive-perfectly-orientable graphs, which remain as open problems.