  We study the Josephson effect in the multiterminal junction of topological
superconductors. We use the symmetry-constrained scattering matrix approach to
derive band dispersions of emergent sub-gap Andreev bound states in a
multidimensional parameter space of superconducting phase differences. We find
distinct topologically protected band crossings that serve as monopoles of
finite Berry curvature. Particularly, in a four-terminal junction the admixture
of $2\pi$ and $4\pi$ periodic levels leads to the appearance of finite energy
Majorana-Weyl nodes. This topological regime in the junction can be
characterized by a quantized nonlocal conductance that measures the Chern
number of the corresponding bands. In addition, we calculate current-phase
relations, variance, and cross-correlations of topological supercurrents in
multiterminal contacts and discuss the universality of these transport
characteristics. At the technical level these results are obtained by
integrating over the group of a circular ensemble that describes the scattering
matrix of the junction. We briefly discuss our results in the context of
observed fluctuations of the gate dependence of the critical current in
topological planar Josephson junctions and comment on the possibility of parity
measurements from the switching current distributions in multiterminal Majorana
junctions.
