A major challenge in synthetic polymers lies in understanding how primary monomer sequence affects materials properties. In this work, we show that charge transport in single molecule junctions of conjugated oligomers critically depends on the primary sequence of monomers. A series of sequence-defined oligomers ranging from two to seven units was synthesized by an iterative approach based on the van Leusen reaction, providing conjugated oligomers with backbones consisting of para-linked phenylenes connected to oxazole, imidazole, or nitro-substituted pyrrole. The charge transport properties of these materials were characterized using a scanning tunneling microscope-break junction (STM-BJ) technique, thereby enabling direct measurement of molecular conductance for sequence-defined dimers, trimers, pentamers, and a heptamer. Our results show that oligomers with specific monomer sequences exhibit unexpected and distinct charge transport pathways that enhance molecular conductance more than 10-fold. A systematic analysis using monomer substitution patterns established that sequence-defined pentamers containing imidazole or pyrrole groups in specific locations provide molecular attachment points on the backbone to the gold electrodes, thereby giving rise to multiple conductance pathways. These findings reveal the subtle but important role of molecular structure including steric hindrance and directionality of heterocycles in determining charge transport in these molecular junctions. This work brings new understanding for designing molecular electronic components.