With both spin and valley degrees of freedom, the low-lying excitonic spectra of photoexcited transition-metal dichalcogenide monolayers (TMDC-MLs) are featured by rich fine structures, comprising the intravalley bright exciton states as well as various intra- and intervalley dark ones. The latter states can be classified as those of the spin- and momentum-forbidden dark excitons according to the violated optical selection rules. Because of their optical invisibility, these two types of the dark states are in principle hardly observed and even distinguished in conventional spectroscopies although their impacts on the optical and dynamical properties of TMDC-MLs have been well noticed. In this Letter, we present a theoretical and computational investigation of the exciton fine structures and the temperature-dependent photoluminescence spectra of strained tungsten diselenide monolayers (WSe2-MLs) where the intravalley spin-forbidden dark exciton lies in the lowest exciton states and other momentum-forbidden states are in the higher energies that are tunable by external stress. The numerical computations are carried out by solving the Bethe-Salpeter equation for an exciton in a WSe2-ML under the stresscontrol in the tight-binding scheme established from the first principle computation in the density functional theory. According to the numerical computation and supportive model analysis, we reveal the distinctive signatures of the spin- and momentumforbidden exciton states of strained WSe2-MLs in the temperature-dependent photoluminescences and present the guiding principle to infer the relative energetic locations of the two types of dark excitons.