The incorporation of nitrogen as a second anion species into oxide glasses offers unique opportunities for modifying glass properties via changes in glass polymerization and structure. In this work, the compositional dependence of elastic properties and the nanoindentation hardness of mixed alkaline-earth silicate oxynitride glasses containing a high amount of nitrogen (>15 at.%, c.a. 35 e/o) were investigated. Three series of silicon oxynitride glass compositions AE–Ca–Si–O–N glasses (where AE = Mg, Sr, and Ba) having varying amounts of modifiers were prepared using a new glass synthesis route, in which a precursor powder of metal hydrides was used. The obtained glasses contained high amounts of N (19 at.%, c.a. 43 e/o) and modifier cations (26 at.%, c.a. 39 e/o). Mg–Ca–Si–O–N glasses had high values of nanohardness (12–16 GPa), along with a reduced elastic modulus (130–153 GPa) and Young’s modulus (127–146 GPa), in comparison with the Sr–Ca- and Ba–Ca-bearing oxynitride glasses. Both the elastic modulus and the nanohardness of AE–Ca–Si–O–N glasses decreased with an increase in the atomic number of the AE element. These property changes followed a linear dependence on the effective cation field strength (ECFS) of the alkaline earth (AE) modifier, according to their valences and ionic radii. No mixed alkaline-earth effect was observed in the current investigation, indicating that the properties were more dictated by the nitrogen content.