Cinnamic acid and acetosyringone recrystallize in vegetable oil as platelets and rods respectively. After dissolution at high temperature(100°C) and upon cooling down to room temperature, their crystallites aggregate into a tenuous network which spans the entire volume of the system even at low mass fraction such as 1%. The whole system behaves as a soft solid characterized by an elastic modulus reaching 1MPa for mass fraction below 10% in the linear regime. The elastic modulus of cinnamic acid based oleogels varies with mass fraction as (-0) 2. For acetosyringone based oleogels, the elastic modulus varies non monotonically with concentration. This has been correlated to a morphological crossover from jammed spherulites at low mass fraction to entangled rods at higher mass fraction. Spherulite formation is related to the presence of branching points along the rods that result from secondary nucleation events. A new empirical parameter is defined from rheological data which reflects how far from equilibrium the solidification proceeds in nonisothermal conditions. This parameter accounts for the different concentration regimes of morphology and rheological properties that have been observed experimentally for acetosyringone.