  We study non-Hermitian higher-order Weyl semimetals (NHHOWSMs) possessing
real spectra and having inversion $\mathcal{I}$ ($\mathcal{I}$-NHHOWSM) or
time-reversal symmetry $\mathcal{T}$ ($\mathcal{T}$-NHHOWSM). When the reality
of bulk spectra is lost, the NHHOWSMs exhibit various configurations of surface
Fermi Arcs (FAs) and Exceptional Fermi Rings (EFRs), providing a setup to
investigate them on an equal footing. The EFRs only appear in the region
between 2nd-order WNs. We also discover Weyl nodes originating from
non-Hermicity, called non-Hermitian Weyl nodes (NHWNs). Remarkably, we find
T-NHHOWSMs which host only 2nd-order NHWNs, having both surface and hinge FAs
protected by the quantized biorthogonal Chern number and quadrupole moment,
respectively. We call this intrinsically non-Hermitian phase exceptional HOWSM.
In contrast to ordinary WNs, the NHWNs can instantly deform to line nodes,
forming a monopole comet. The NHWNs also show exceptional tilt-rigidity, which
is a strong resistance towards titling due to attachment to exceptional
structures. This phenomenon can be a promising experimental knob. Finally, we
reveal the exceptional stability of FAs called exceptional helicity. Surface
FAs having opposite chirality can live on the same surface without gapping out
each other due to the complex nature of the spectrum. Our work motivates an
immediate experimental realization of NHHOWSMs.
