  We present the first theoretical study of transport properties of Weyl
semimetals with point defects. Focusing on a class of time-reversal symmetric
Weyl lattice models, we show that dilute lattice vacancies induce a finite
density of quasi-localized states at and near the nodal energy, causing strong
modifications to the low-energy spectrum. This generates novel transport
effects, namely (i) an oscillatory behaviour of the dc-conductivity with the
charge carrier density in the absence of magnetic fields, and (ii) a
plateau-shaped dissipative optical response for photon frequencies below the
inter-band threshold, $E_{F}\!\lesssim\!\hbar\omega\!\lesssim\!2E_{F}$.Our
results provide a path to engineer unconventional quantum transport effects in
Weyl semimetals by means of common point defects.
