Edit: The situation seems to be the following: For Kac-Moody algebras, there is a unique conjugacy class of Cartan subalgebra (under automorphisms), and the Weyl group acts transitively on systems of simple roots. These properties fail to hold in the superalgebra setting. One instead can form a groupoid whose objects are finite size square matrices $A$ with integer entries (or the Lie superalgebras $g(A)$ obtained by a generators-and-relations construction), and whose morphisms from $A$ to $A'$ are superalgebra isomorphisms $g(A) \to g(A')$ that take a Cartan of $g(A)$ to a Cartan of $g(A')$. The Weyl groupoid of $g(A)$ is then the connected component of $A$ in the larger groupoid.