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In general, the vector sum of the external torques equals $\mathrm{d}\mathbf{L}/\mathrm{d}t$, the rate of change of the angular momentum vector. If your object is starting at rest, the instantaneous axis of rotation will be in the direction of $\mathrm{d}\mathbf{L}/\mathrm{d}t$. Otherwise, it will be in the direction of $\mathbf{L}$, which may be changing with time. Note: a torque relative to the center of mass is given by $\mathbf{r}\times \mathbf{F}$ (vector product).