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We investigate the individual and combined effects of substitutional Mn-doping and strain engineering in monolayers of MoS2 and MoSe2, using density functional theory (DFT) to examine the structural, electronic, and magnetic properties. Doping with Mn is shown to introduce magnetic character by producing localized spin polarization in the region near the defect. The Mn dopants preferentially couple ferromagnetically due to an interaction that is described as double exchange. Additionally, doping with Mn changes the electronic structure by introducing defect states within the band gap, which according to one form of DFT, results in half-metallic character. Compressive and tensile strain both decrease the band gap in the pure transition metal dichalcogenides (TMDs), retaining the materials' semiconducting character. Strain has a multi-varied effect on the electronic properties in the Mn-doped TMDs. Tensile strain demonstrates potential to strengthen ferromagnetic coupling, offering new possibilities for strain-engineering dilute magnetic semiconductors with more enhanced stability at room temperature. [ABSTRACT FROM AUTHOR]