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 nonstandard contributions to neutrinoless double beta decay via long-range λ and η neutrino exchange. © 2016 American Physical Society.