NOVELTY - Heterogeneous catalyst system comprises: at least one metal oxide including zinc oxide, nickel oxide, silicon dioxide, titanium dioxide, neodymium oxide, ytterbium oxide, cerium oxide, aluminum oxide and/or lanthanum oxide; and an oxide support including zirconium oxide and/or hydrous zirconium oxide, where the metal oxide and the oxide support interact so that the metal oxide is chemically stable and has durability in an acidic chemical stream.    USE - The heterogeneous catalyst system is useful: for facilitating esterification or transesterification reactions in an acidic chemical stream; and in forming a biodiesel product from the unrefined or waste oils (all claimed).    ADVANTAGE - The heterogeneous catalyst system: exhibits high catalytic activity for esterification or transesterification reactions; has high durability with respect to long-term performance; can be effectively used with a low grade oil feed stock containing free fatty acids and water; is insensitive to the presence of water arising from the esterification of the free fatty acids and alcohols; provides high yields of fatty acid methyl ester products even when the feed streams have a low methanol to oil ratio; provides biodiesel product at low cost; exhibits low acid strength, thus avoiding undesirable side reaction including alcohol dehydration or cracking of fatty acids; and is chemically stable.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are also included for:    (1) forming the heterogeneous catalyst system, comprising: providing at least one metal salt; dissolving the metal salt in a liquid to form an acidic or basic metal salt solution; providing a zirconium medium, which is either zirconium oxide particles or a zirconium salt precursor that forms zirconium oxide supported metal oxides particles; combining the metal salt solution with the zirconium medium; forming at least one metal oxide incorporated into the structure of the zirconium oxide particles to form a metal oxides/zirconium oxide catalyst using a sol-gel condensation process, impregnation process, or co-precipitation process; recovering the metal oxides/zirconium oxide catalyst from the solution; allowing the metal oxides/ zirconium oxide catalyst to age for a predetermined amount of time at a predetermined temperature; pelletizing the metal oxides/zirconium oxide catalyst into a desired shape or size; and calcining the metal oxides/zirconium oxide catalyst at an elevated temperature for at least 30 minutes;    (2) a biodiesel product formed by reacting an unrefined or waste oil with an alcohol in the presence of the heterogeneous catalyst system; and    (3) a method (M1) of forming the biodiesel product from unrefined or waste oils, comprising: (a) preparing the heterogeneous catalyst system; (b) placing an unrefined or waste oil feedstock and an alcohol in contact with the catalyst system to form a reaction mixture comprising the oil and alcohol, along with free fatty acids, water, or other impurities; (c) heating the reaction mixture to 130-250 degrees C; (d) allowing the transesterification of the oil and the esterification of the fatty free acids to simultaneously occur for a predetermined amount of time to form fatty acid methyl esters resulting in the biodiesel product; and (e) separating the catalyst from the biodiesel product to collect the biodiesel product.