When considering transition-metal dichalcogenides (TMDCs) in van der Waals heterostructures for periodic ab initio calculations, usually, lattice mismatch is present, and the TMDC needs to be strained. In this study we provide a systematic assessment of biaxial strain effects on the orbital, spin-orbit, and optical properties of the monolayer TMDCs using ab initio calculations. We complement our analysis with a minimal tight-binding Hamiltonian that captures the low-energy bands of the TMDCs around the K and K' valleys. We find characteristic trends of the orbital and spin-orbit parameters as a function of the biaxial strain. Specifically, the orbital gap decreases linearly, while the valence (conduction) band spin splitting increases (decreases) nonlinearly in magnitude when the lattice constant increases. Furthermore, employing the Bethe-Salpeter equation and the extracted parameters, we show the evolution of several exciton peaks, with biaxial strain, on different dielectric surroundings, which are particularly useful for interpreting experiments studying strain-tunable optical spectra of TMDCs.