The brain has the ability to learn and evaluate as it receives and registers information. Signals between neurons are transmitted via synapses whose plasticity is modulated by usage. A bio-realistic electrical analog is a second-order memristor, where the short-term internal dynamics influence the long-term state. It is achieved here with an all-oxide multiferroic tunnel junction: La0.7Sr0.3MnO3 / BaTiO3 / La0.7Sr0.3MnO3. Similar to the modulation of synaptic weight by stimuli, multi-levels of resistance may be encoded by mean of voltage pulses, on long time scale and in correlation with short-term effects. Neuromimetic learning functions are demonstrated: short and long-term potentiation/depression, paired-pulse facilitation/depression, spike-rate- and experience-dependent plasticity. The threshold frequency of pulse trains at which depression changes into potentiation depends on the previous activity, with a sliding effect as in neurobiology. The voltage pulses induce reversible changes of both dielectric polarization and oxygen vacancies distribution, generating transient trapped/detrapped charges at the two interfaces that govern the dynamic response. The resistance levels are determined by the final cationic ordering (the redox Mn3+/Mn4+ ratio) at the two interfacial layers. The stimulation/relaxation dynamics are close to that in biological counterparts. Such memristors can be used in hardware artificial networks for advanced processing/storage of the information.