  Skyrmions are small magnetic quasiparticles, which are uniquely characterized
by their topological charge and their helicity. In this Rapid Communication, we
show via calculations how both properties can be determined without relying on
real-space imaging. The orbital magnetization and topological Hall conductivity
measure the arising magnetization due to the circulation of electrons in the
bulk and the occurrence of topologically protected edge channels due to the
emergent field of a skyrmion crystal. Both observables quantify the topological
Hall effect and distinguish skyrmions from antiskyrmions by sign. Additionally,
we predict a magnetoelectric effect in skyrmion crystals, which is the
generation of a magnetization (polarization) by application of an electric
(magnetic) field. This effect is quantified by spin toroidization and
magnetoelectric polarizability. The dependence of the transverse
magnetoelectric effect on the skyrmion helicity fits that of the classical
toroidal moment of the spin texture and allows to differentiate skyrmion
helicities: it is largest for Bloch skyrmions and zero for Neel skyrmions. We
predict distinct features of the four observables that can be used to detect
and characterize skyrmions in experiments.
