This paper presents novel treatments for the Ellis non-Newtonian nanofluids flow over a rotating cone in the presence of motile oxytactic microorganisms. These treatments are depending on solutions of the stress tensor equations at specific values of the power-law index α (α = 0,0.5,1,2) and introducing the stress as expressions in terms of the velocity gradients. Here, four systems of the governing equations for each value of α are presented and the non-similar forms for these systems are obtained. An efficient finite difference method based on the Blottner technique is applied to solve the converted systems. Various important impacts are examined in these simulations such as, magnetic field, non-linear radiation, viscous dissipation, heat generation and Joule heating. Wide ranges of the non-similar parameters are considered, namely, 0 ≤ ξ ≤ 10, 0 ≤ η ≤ 35. The major results revealed that, the skin friction gets higher values at the Ellis case α = 2 while the Newtonian nanofluids α = 1 gives the highest heat transfer rate. Both the velocity and temperature gradients are diminishing as the bioconvection Rayleigh number is enhanced.