  We study the dual description of the $\eta$-deformed $OSP(N|2m)$ sigma model
in the asymptotically free regime ($N>2m+2$). Compared to the case of classical
Lie groups, for supergroups there are inequivalent $\eta$-deformations
corresponding to different choices of simple roots. For a class of such
deformations we propose the system of screening charges depending on a
continuous parameter $b$, which defines the $\eta$-deformed $OSP(N|2m)$ sigma
model in the limit $b\rightarrow\infty$ and a certain Toda QFT as
$b\rightarrow0$. In the sigma model regime we show that the leading UV
asymptotic of the $\eta$-deformed model coincides with a perturbed Gaussian
theory. In the perturbative regime $b\rightarrow0$ we show that the tree-level
two-particle scattering matrix matches the expansion of the trigonometric
$OSP(N|2m)$ $S$-matrix.
