We attempt to determine the relative fraction of stars that have undergone significant radial migration by studying the orbital properties of metal-rich ([Fe/H]$>0.1$) stars within 2 kpc of the Sun using a sample of more than 3,000 stars selected from iDR4 of the Gaia-ESO Survey. We investigate the kinematic properties, such as velocity dispersion and orbital parameters, of stellar populations near the sun as a function of [Mg/Fe] and [Fe/H], which could show evidence of a major merger in the past history of the Milky Way. This was done using the stellar parameters from the Gaia-ESO Survey along with proper motions from PPMXL to determine distances, kinematics, and orbital properties for these stars to analyze the chemodynamic properties of stellar populations near the Sun. Analyzing the kinematics of the most metal-rich stars ([Fe/H]$>0.1$), we find that more than half have small eccentricities () or are on nearly circular orbits. Slightly more than 20% of the metal-rich stars have perigalacticons $Rp>7$ kpc. We find that the highest [Mg/Fe], metal-poor populations have lower vertical and radial velocity dispersions compared to lower [Mg/Fe] populations of similar metallicity by $\sim 10$ km s$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$. The median eccentricity increases linearly with [Mg/Fe] across all metallicities, while the perigalacticon decreases with increasing [Mg/Fe] for all metallicities. Finally, the most [Mg/Fe]-rich stars are found to have significant asymmetric drift and rotate more than 40 km s$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ slower than stars with lower [Mg/Fe] ratios. While our results cannot constrain how far stars have migrated, we propose that migration processes are likely to have played an important role in the evolution of the Milky Way, with metal-rich stars migrating from the inner disk toward to solar neighborhood and past mergers potentially driving enhanced migration of older stellar populations in the disk.