Equiatomic NiCoCr solid solutions have been shown by recent experiments and atomistic simulations to display exceptional mechanical properties that have been suggested to be linked to nanostructural short-range order (SRO) features that may arise from thermal treatments, such as annealing or/and aging. Here we use hybrid Monte Carlo-molecular dynamics simulations to gain further insights of thermal effects on the SRO formation as well as the edge dislocation plasticity mechanisms of equiatomic NiCoCr face-centered cubic solid solution. For that purpose, we utilize two well-known NiCoCr interatomic potentials, one of which displays well-documented SRO, believed to be linked to experimental evidence and labeled as the Li-Sheng-Ma potential, while the other (Farkas-Caro) does not. We use these two potentials to discern short-range ordering (from inherent randomness in random solid solutions) and understand how SROs influence dislocation depinning dynamics in various thermal annealing scenarios. In this context, we used robust, scale-dependent metrics to infer a characteristic SRO size in the Li-Sheng-Ma case by probing local concentration fluctuations which otherwise indicate uncorrelated patterns in the Farkas-Caro case in a close agreement with random alloys. Our Voronoi-based analysis shows meaningful variations of local misfit properties owing to the presence of SROs. Using relevant order parameters, we also report on the drastic increase of chemical ordering within the stacking fault region. More importantly, we find that the Li-Sheng-Ma potential leads to excellent edge dislocation depinning strength with low stacking fault width. Our findings indicate an enhanced roughening mechanism due to the SROs-misfit synergy that leads to significant improvements in dislocation glide resistance. We argue that the improvements in alloy strength have their atomistic origins in the interplay between nanoscopic SROs and atomic-level misfit properties.