Altermagnets with nonrelativistic spin-valley coupling provide an ideal platform for integrating spintronics and valleytronics. Moreover, breaking the symmetry of the system via external stimuli is expected to induce exotic physical phenomena by tuning the spin-valley coupling, opening opportunities for exploring multifunctional applications of such altermagnets. In this work, using first-principles calculations, we propose that the two-dimensional Janus Co2OSe monolayer is a promising altermagnet exhibiting spin-valley coupling. It features a pair of degenerate valleys at the high-symmetry X and Y points with opposite spin polarizations, protected by [C2||M] symmetry. Upon applying uniaxial strain, valley polarization emerges due to the breaking of mirror symmetry, with its magnitude reaching 121.9 meV and its sign depending on the strain type (tensile or compressive) and direction. The strain-induced valley polarization, combined with the valley-contrasting Berry curvature, enables the system to exhibit the anomalous valley Hall effect. Hole doping under uniaxial strain can induce a net magnetic moment in the Co2OSe monolayer, giving rise to the piezomagnetic effect. Furthermore, noncollinear spin current can be generated in the monolayer when an in-plane electric field is applied under hole doping conditions. These findings not only broaden the scope of altermagnets featuring spin-valley coupling but also lay the material foundation for developing novel, high-performance, multifunctional micro- and nanoscale devices.