  We study the effect of a perpendicular magnetic fieldBon a multinode Weyl
semimetal (mWSM)of arbitrary integer monopole chargen, with the two Weyl
multinodes separated ink-space. Besides type-I mWSMs, there exist type-II mWSMs
which are characterized by the tilted minimal dispersion for low-energy
excitations; the Weyl points in type-II mWSMs are still protected crossings but
appear at the contact of the electron and hole pockets, after the Lifshitz
transition. We find that the presence of a perpendicular magnetic field
quantizes the occupation pockets due to the presence of Fermi tubes. In this
theory, the Hilbert space is spanned by a set of $n$ chiral degenerate
groundstates, and a countably infinite number of particle-hole symmetric Landau
levels. We calculate the Hall conductivity for the tilt-symmetric case of
type-I mWSM using the Kubo formula, in the zero-frequency (DC) limit, and
recover the well-known vacuum contribution. We compute the Fermi surface
corrections and show that the expression generalizes from the formula for
elementary ($n=1$) type-I WSMs. We derive an expression for the type-II mWSM
Hall conductivity, which is bounded by a Landau level cutoff introduced on
physical grounds. Interestingly, we find that the anomalous vacuum Hall
conductivity is vanishing in the type-II phase at all temperatures. The
corresponding thermal Hall and Nernst conductivities are evaluated and
characterized for both phases. The qualitative and quantitative observations
presented here may serve in the characterization of generic mWSMs of both
types.
