  We study strongly graded groupoids, which are topological groupoids $\mathcal
G$ equipped with a continuous, surjective functor $\kappa: \mathcal G \to
\Gamma$, to a discrete group $\Gamma$, such that
$\kappa^{-1}(\gamma)\kappa^{-1}(\delta) = \kappa^{-1}(\gamma \delta)$, for all
$\gamma, \delta \in \Gamma$. We introduce the category of graded $\mathcal
G$-sheaves, and prove an analogue of Dade's Theorem: $\mathcal G$ is strongly
graded if and only if every graded $\mathcal G$-sheaf is induced by a $\mathcal
G_{\epsilon}$-sheaf. The Steinberg algebra of a graded ample groupoid is
graded, and we prove that the algebra is strongly graded if and only if the
groupoid is. Applying this result, we obtain a complete graphical
characterisation of strongly graded Leavitt path and Kumjian-Pask algebras.
