In this paper, the electronic band structure, Rashba effect, hexagonal warping, and piezoelectricity of Janus group-VIA binary monolayers STe2, SeTe2, and Se2Te are investigated based on density functional theory (DFT). Due to the inversion asymmetry and spin-orbit coupling (SOC), the STe2, SeTe2 and Se2Te monolayers exhibit large intrinsic Rashba spin splitting (RSS) at the Γ point with the Rashba parameters 0.19 eV Å, 0.39 eV Å, and 0.34 eV Å, respectively. Interestingly, based on the k·p model via symmetry analysis, the hexagonal warping effect and a nonzero spin projection component Sz arise at a larger constant energy surface due to nonlinear k3 terms. Then, the warping strength λ was obtained by fitting the calculated energy band data. Additionally, in-plane biaxial strain can significantly modulate the band structure and RSS. Furthermore, all these systems exhibit large in-plane and out-of-plane piezoelectricity due to inversion and mirror asymmetry. The calculated piezoelectric coefficients d11 and d31 are about 15-40 pm V-1 and 0.2-0.4 pm V-1, respectively, which are superior to those of most reported Janus monolayers. Because of the large RSS and piezoelectricity, the studied materials have great potential for spintronic and piezoelectric applications.