Due to the asymmetric structures, two-dimensional Janus materials have gained significant attention in research for their intriguing piezoelectric and spintronic properties. In the present work, quintuple Bi2X3 (X = S, Se) monolayers (MLs) have been modified to create stable Janus Bi2X2Y (X not equal Y = S, Se) MLs that display piezoelectricity in both the planes along with Rashba effect. The out-of-plane piezoelectric constant (d(33)) is 41.18 (-173.14) pm V-1, while the in-plane piezoelectric constant (d(22)) is 5.23 (6.21) pm V-1 for Janus Bi2S2Se (Bi2Se2S) ML. Including spin-orbit coupling in the Janus MLs results in anisotropic giant Rashba spin splitting (RSS) at the Gamma point in the valence band, with RSS proportional to d33. The Rashba constant along the Gamma-K path, alpha(Gamma-K)(R), is 3.30 (2.27) eV angstrom, whereas along Gamma-M, alpha(Gamma-M)(R) R is 3.58 (3.60) eV angstrom for Janus Bi2S2Se (Bi2Se2S) ML. The MLs exhibit ultrahigh electron mobility (similar to 5442 cm(2) V-1 s(-1)) and have electron to hole mobility ratio of more than 2 due to their tiny electron-effective masses. The flexibility of the MLs allows for a signification alteration in its properties, like band gap, piezoelectric coefficient, and Rashba constant, via mechanical (biaxial) strain. For the MLs, band gap and d(33) value are enhanced with compressive strain. The d(33) value of Janus Bi2Se2S reaches 4886.51 pm V-1 under compressive strain. The coexistence of anisotropic colossal out-of-plane piezoelectricity, giant RSS, and ultrahigh carrier mobilities in Janus Bi2S2Se and Bi2Se2S MLs showcase their tremendous prospects in nanoelectronic, piezotronics, and spintronics devices.