The model for ordering of triangular-shaped molecules with strongly interacting vertices is proposed and solved by the Monte Carlo method. The model accounts for three main intermolecular interactions and three states (two main orientations and a vacancy state) of a molecule on triangular lattice, the situation which is encountered in self-assembly of TMA molecules characterized by strongly directional H-bonding. Distinguishing the main "tip-to-tip" interaction, we calculate the phase diagrams for the honeycomb and frustrated honeycomb structures and demonstrate how these structures shrink and vanish with gradual increase of two other ("side-to-side" and "tip-to-side") interactions. We study the effect of frustration on the phase diagram, since the frustrated phase is obtained at the Ising limit of the model. We also demonstrate how the inclusion of longer-range interactions leads to substitution of the frustrated phase by the zigzag structure. Finally, we obtain the phase diagram with two experimentally found TMA structures (honeycomb and zigzag) and discuss the conditions of their existence by comparison with the experimental results.