  We construct and classify $(1 \; 2\; \cdots \; k)$-twisted $V^{\otimes
k}$-modules for $k$ odd and for $V$ a vertex operator superalgebra. This
extends previous results of the author, along with Dong and Mason, classifying
all permutation-twisted modules for tensor product vertex operator algebras, to
the setting of vertex operator superalgebras for odd order permutations. We
show why this construction does not extend to the case of permutations of even
order in the superalgebra case and how the construction and classification in
the even order case is fundamentally different than that for the odd order
permutation case. We present a conjecture made by the author and Nathan Vander
Werf concerning the classification of permutation twisted modules for
permutations of even order.
