We interpret the 2 TeV excesses at the LHC in a left-right symmetric model with Higgs doublets and spontaneous D-parity violation. The light neutrino masses are understood via a linear seesaw, suppressed by a high D-parity breaking scale, and the heavy neutrinos have a pseudo-Dirac character. In addition, with a suppressed right-handed gauge coupling gR/gL ≈ 0.6 in an SO(10) embedding, we can thereby interpret the observed eejj excess at CMS. We show that it can be reconciled with the diboson and dijet excesses within a simplified scenario based on our model. Moreover, we find that the mixing between the light and heavy neutrinos can be potentially large which would induce dominant non-standard contributions to neutrinoless double beta decay via long-range λ and η neutrino exchange.