Short version: Which term generalizes "polyhedron" to include shapes whose faces are not necessarily flat?
Long version:
The finite volume method is not very restrictive when it comes to the shape of the grid cells. OpenFOAM (a library that implements FVM), for example, requires that a cell be "contiguous, convex and closed" and defined as "a list of faces". A face is defined by a "list of points such that each two neighbouring points are connected by an edge"; the face center "needs to be inside the face", and not "all points of the face need to be coplanar".
First I thought of describing the class of allowed shapes for a cell as "polyhedra". However, a polyhedron must have flat faces, which is not a requirement for the cell. I wonder if "warped polyhedra" would better describe the shape or if there is an appropriate geometrical term for that class.
Such faces (rank 2 faces which don't lie in a 2-dimensional plane, or more generally rank-$j$ faces which don't lie in a $j$-dimensional subspace) are commonly called "skew faces". Often they are conceived as "skeletal", so they consist solely of a set of vertices and the edges between them, not necessarily lying in a single plane. It sounds like you want the faces to also include a surface bounded by the straight line-segment edges. Then you need to decide whether or not you want to allow the surfaces to intersect or overlap.
A polyhedron made up of such skew faces can be called a skew polyhedron. Wikipedia has an article on regular skew polyhedra. See also Skew polygon.