This work presents two searches for new physics characterized by pair-production of strongly interacting particles, each decaying to hadronic jets and a particle that is not detectable. The searches use the full 13 TeV proton-proton collision dataset produced by CERN's Large Hadron Collider and recorded by the CMS detector from 2016 to 2018, with total integrated luminosity 137 fb-1. The presence of particles interacting too weakly to be detected is inferred using imbalance in the transverse momentum of the collision products, and sensitivity to pair-production is enhanced by requiring large values of the kinematic variable MT2 in events with at least two jets. The first search is inclusive, binning events using the total hadronic transverse energy, the total number of jets, the number of jets reconstructed as originating from a bottom quark, and either the value of MT2 in multijet events, or the transverse momentum of the jet in monojet events. The second search extends the first, by requiring the presence of a disappearing track in the event, and adds binning in the length and transverse momentum of the disappearing track. Both searches are sensitive to a variety of extensions to the Standard Model that include dark matter candidates. Of greatest interest, the results set constraints on pair production of squarks and gluinos as predicted by R-parity conserving supersymmetric extensions of the Standard Model, in which the lightest supersymmetric particle is a neutralino. The first search is sensitive to any decay chain terminating in Standard Model hadrons plus the neutralino, while the second specifically targets, with greatly enhanced sensitivity, decay chains containing an intermediate long-lived chargino. These constraints are the most stringent yet produced by any experiment.