  A Weyl semimetal (WSM)\ is a three-dimensional topological phase of matter
where pairs of nondegenerate bands cross at isolated points in the Brillouin
zone called Weyl nodes. Near these points, the electronic dispersion is gapless
and linear. A magnetic field $B$ changes this dispersion into a set of Landau
levels which are dispersive along the direction of the magnetic field only. The
$n=0$ Landau level is special since its dispersion$\ $is linear and
unidirectional. The presence of this chiral level distinguishes Weyl from
Schr\"{o}dinger fermions. In this paper, we study the quantum oscillations of
the orbital magnetization and magnetic susceptibility in Weyl semimetals. We
generalise earlier works% \cite{Mikitik2019} on these De Haas-Van Alphen
oscillations by considering the effect of a tilt of the Weyl nodes. We study
how the fundamental period of the oscillations in the small $B$ limit and the
strength of the magnetic field $B_{1}$ required to reach the quantum limit are
modified by the magnitude and orientation of the tilt vector $\mathbf{t}$. We
show that the magnetization from a single node is finite in the $B\rightarrow
0$ limit. Its sign depends on the product of the chirality and sign of the tilt
component along the magnetic field direction. We also study the magnetic
oscillations from a pair of Weyl nodes with opposite chirality and with
opposite or identical tilt. Our calculation shows that these two cases lead to
a very different behavior of the magnetization in the small and large $B$
limits. We finally consider the effect of an energy shift $\pm \Delta _{0}$ of
a pair of Weyl nodes on the magnetic oscillations. We assume a constant density
of carriers so that both nodes share a common Fermi level. Our calculation can
easily be extended to a WSM with an arbitrary number of pairs of Weyl nodes.
