We define an invariant of welded virtual knots from each finite crossed module by considering crossed module invariants of ribbon knotted surfaces which are naturally associated with them. We elucidate that the invariants obtained are non-trivial by calculating explicit examples. We define welded virtual graphs and consider invariants of them defined in a similar way.

For $q$ a non-negative integer, we introduce the internal $q$-homology of crossed modules and we obtain in the case $q=0$ the homology of crossed modules. In the particular case of considering a group as a crossed module we obtain that its internal $q$-homology is the homology of the group with coefficients in the ring of the integers modulo $q$.

The second internal $q$-homology of crossed modules coincides with the invariant introduced by Grandjeán and López, that is, the kernel of the universal $q$-central extension. Finally, we relate the internal $q$-homology of a crossed module to the homology of its classifying space with coefficients in the ring of the integers modulo $q$.

AMS 2000 Mathematics subject classification: Primary 18G50; 20J05. Secondary 18G30