With the increase in global demand for biodiesel, first generation feedstock has drawn the attention of governmental institutions due to the correlation with large land farming areas. The second and third feedstock generations are greener feedstock sources, nevertheless, they require different catalytic conditions if compared with first generation feedstock. In this work, we present the synthesis and characterization of oligoesters matrices and their functionalization to act as a pseudo-homogeneous acid catalyst for biodiesel production, named Oligocat. The main advantage of Oligocat is given due to its reactional medium interaction. Initially, oligocat is a solid catalyst soluble in the alcoholic phase, acting as a homogeneous catalyst, providing better mass transfer of the catalytic groups to the reaction medium, and as the course of the reaction happens, Oligocat migrates to the glycerol phase, also providing the advantage of easy separation of the biodiesel. Oligocat was synthesized through polymerization of aromatic hydroxy acids, followed by a chemical functionalization applying the sulfonation technique. Characterization of the catalysts was carried out by infrared spectroscopy (FTIR), nuclear magnetic resonance spectroscopy (NMR), gel permeation chromatography (GPC), and thermogravimetric analysis (TGA). The synthesized oligomers presented 5357 g·mol−1 (Mw) and 3909 g·mol−1 (Mn), with a moderate thermal resistance of approximately 175 °C. By sulfonation reaction, it was possible to obtain a high content of sulphonic groups of nearly 70 mol%, which provided the catalytic activity to the oligomeric matrix. With the mentioned physical–chemical properties, Oligocat is chemically designed to convert second generation feedstock to biodiesel efficiently. Preliminary investigation using Oligocat for biodiesel production resulted in conversion rates higher than 96.5 wt.%.