  We extend our previous work from arXiv:1903.06863 on biquandle module
invariants of oriented surface-links to the case of unoriented surface-links
using bikei modules. The resulting infinite family of enhanced invariants
proves be effective at distinguishing unoriented and especially non-orientable
surface-links; in particular, we show that these invariants are more effective
than the bikei homset cardinality invariant alone at distinguishing
non-orientable surface-links. Moreover, as another application we note that our
previous biquandle modules which do not satisfy the bikei module axioms are
capable of distinguishing different choices of orientation for orientable
surface-links as well as classical and virtual links.
