  Pursuing complementary field-theoretic and numerical methods, we here paint
the global phase diagram of a three-dimensional dirty Weyl system. The
generalized Harris criterion, augmented by a perturbative renormalization-group
(RG) analysis shows that weak disorder is an irrelevant perturbation at the
Weyl semimetal(WSM)-insulator quantum critical point (QCP). But, a metallic
phase sets in through a quantum phase transition (QPT) at strong disorder
across a multicritical point (MCP). The field theoretic predictions for the
correlation length exponent $\nu=2$ and dynamic scaling exponent $z=5/4$ at
this MCP are in good agreement with the ones extracted numerically, yielding
$\nu=1.98 \pm 0.10$ and $z=1.26 \pm 0.05$, from the scaling of the average
density of states (DOS). Deep inside the WSM phase, generic disorder is also an
irrelevant perturbation, while a metallic phase appears at strong disorder
through a QPT. We here demonstrate that in the presence of generic, but strong
disorder the WSM-metal QPT is ultimately always characterized by the exponents
$\nu=1$ and $z=3/2$ (to one-loop order), originating from intra-node or chiral
symmetric (e.g., regular and axial potential) disorder. We here anchor such
emergent \emph{chiral superuniversality} through complementary RG calculations,
controlled via $\epsilon$-expansions, and numerical analysis of average DOS
across WSM-metal QPT. In addition, we also discuss a subsequent QPT (at even
stronger disorder) of a Weyl metal into an Anderson insulator by numerically
computing the typical DOS at zero energy. The scaling behavior of various
physical observables, such as residue of quasiparticle pole, dynamic
conductivity, specific heat, Gr$\ddot{\mbox{u}}$neisen ratio, inside various
phases as well as across various QPTs in the global phase diagram of a dirty
Weyl liquid are discussed.
