This paper aims to present a comprehensive study of the non-linear peristaltic transport within a vertical uniform/non-uniform channel filled with a Jeffery non-Newtonian nanofluids in the presence of oxytactic microorganisms. The thermal conductivity of the used physiological fluids is varied linearly with the temperature while Arrhenius function is applied for the activation energy. The significance of electrical and magnetic fields together with a linear radiation and viscous dissipation are analyzed. The flow and heat transfer analysis has been performed under wall slip and compliant conditions. Additionally, optimization of the system entropy under the impacts of these aspects is examined. Numerical solutions for the governing system are introduced and profiles of the velocity 𝑢, temperature 𝜃, nanoparticle distributions 𝜑, heat transfer coefficient 𝑧 and extra stress tensor distribution 𝑆𝑥𝑦 for the variations of the considered parameters are discussed. The main outcomes revealed that the maximizing of the Brinkman number 𝐵𝑟 is better to get higher features of the extra stress tensor 𝑆𝑥𝑦. Also, the velocity 𝑢, density of the microorganisms 𝜉 and the NP distributions in the interval −0.5 < 𝑦 < 0.5 get lower features as 𝑚𝑒 is altered. However, the temperature distributions are maximized as 𝑚𝑒 is growing.