Low-temperature (∼20 K) electron irradiation with 2.5 MeV relativistic electrons was used to study the effect of controlled nonmagnetic disorder on the normal and superconducting properties of the type-II Dirac semimetal PdTe2. We report measurements of longitudinal and Hall resistivity, thermal conductivity and London penetration depth using the tunnel-diode resonator technique for various irradiation doses. The normal-state electrical resistivity follows the Matthiessen rule with an increase of the residual resistivity at a rate of ∼0.77μΩcm/(C/cm2). London penetration depth and thermal conductivity results show that the superconducting state remains fully gapped. The superconducting transition temperature is suppressed at a nonzero rate that is about 16 times slower than described by the Abrikosov-Gor'kov dependence, applicable to magnetic impurity scattering in isotropic, single-band s-wave superconductors. To gain information about the gap structure and symmetry of the pairing state, we perform a detailed analysis of these experimental results based on insight from a generalized Anderson theorem for multiband superconductors. This imposes quantitative constraints on the gap anisotropies for each of the possible pairing candidate states. We conclude that the most likely pairing candidate is an unconventional A+−1g state. While we cannot exclude the conventional A++1g and the triplet A1u, we demonstrate that these candidates require additional assumptions about the orbital structure of the disorder potential to be consistent with our experimental results, e.g., a ratio of inter- to intraband scattering for the singlet state significantly larger than 1. Due to the generality of our theoretical framework, we believe that it will also be useful for irradiation studies in other spin-orbit-coupled multiorbital systems.