  We present a general method for constructing effective field theories for
non-relativistic superfluids, generalizing the previous approaches of Greiter,
Witten, and Wilczek, and Son and Wingate to the case of several superfluids in
solution. We investigate transport in mixtures with broken parity and find a
parity odd "Hall drag" in the presence of independent motion as well as a
pinning of mass, charge, and energy to sites of nonzero relative velocity. Both
effects have a simple geometric interpretation in terms of the signed volumes
and directed areas of various sub-complexes of a "velocity polyhedron": the
convex hull formed by the endpoints of the velocity vectors of a superfluid
mixture. We also provide a simple quasi-one-dimensional model that exhibits
non-zero Hall drag.
