Charge transport in single molecule junctions critically depends on the chemical identity of anchor groups used to connect molecular wires to electrodes. In this work, we report the charge transport properties of conjugated oligomers with oxazole anchors, focusing on the role of the heteroatom substitution position in terminal oxazole groups. Our results show that oxazole serves as an efficient anchor group to form stable gold-molecule-gold junctions. We further observe quantum interference (QI) effects in oxazole-terminated phenylene molecular junctions, including destructive QI in meta-substituted phenyl rings and constructive QI in para-substituted phenyl rings containing terminal oxazole groups with the same chemical constitution on both termini (i.e., O5O5 (5-oxazolyl) or O4O4 (4-oxazolyl) linkages on both termini). Surprisingly, meta-substituted phenyl rings with nonequivalent constitutions (i.e., O4O5 oxazole terminal linkages) show unexpectedly higher conductance as compared to para-substituted analogues. These results suggest that charge transport in oxazole-terminated molecules is determined by the heteroatom substitution position of the oxazole anchor in addition to the aryl substitution pattern of the π-conjugated core. Our results further show that conjugated molecules with homogeneous oxazole linkages obey a quantum circuit rule such that GO4-p-O4/GO4-m-O4 = GO5-p-O5/GO5-m-O5, where G is molecular conductance. Overall, our work provides key insight into the development of new chemistries for molecular circuitry in the rapidly advancing field of single molecule electronics.