Tunable and uniform evolution of conductance is the key performance metric for neuromorphic computing leveraging memristors. Nonetheless, the stochastic conductance update associated with limited material composition and uncontrollable filament distribution has restricted the tunability that can be customized for targeted synaptic properties. Here, we introduce organic heterojunction memristors utilizing the C60/P3HT bilayer, demonstrating analog switching characteristics with multilevel conductance states. We demonstrate that both conventional bipolar and unipolar voltages can achieve synaptic plasticity modulation for potentiation and depression, offering enhanced tunability. Through in situ Raman spectroscopy and impedance spectroscopy, we directly observe the dynamic alterations within the active layers during switching processes. The reversible migration of ions diminishes the barrier within the polymer layer, leading to highly uniform resistive switching behavior. The C60 layer functions as a confined transport medium, mitigating critical current variability issues. Moreover, we introduce a shunt resistor approach, furnishing analog memristors with selectively adjustable uniformity, enhanced linearity, and expanded dynamic conductance range, providing a general solution adaptable to various memristive hardware architectures.