All-optical switching and multiple logic gates are experimentally demonstrated using AlGaInAs/InP hybrid square-rectangular lasers. Controllable bistability induced by saturable absorption in the square microcavity is achieved around the threshold with the square cavity in an open circuit state. Based on the bistability, all-optical switching operation is realized by injecting set/reset optical signals with the wavelengths around the lasing mode of 1529.9 nm and another high-Q mode at 1560 nm. Furthermore, mode competitions between three resonant modes around 1541 nm with an interval of 1.2 nm are used to realize all-optical multiple logic gates of NOT, NOR, and NAND functions under low-power optical pulses, with injecting currents to the square and rectangular sections. The static extinction ratio of 34, 40 and 24 dB are obtained for NOT, NOR, and NAND gates, respectively, and the dynamic extinction ratio over 10 dB of NOT function at 15 Gb/s, NOR and NAND functions at 2 Gb/s are demonstrated. With the merits of multifunctional operations, large optical injection wavelength tolerant ranges, low power consumption, small footprint and suitability for on-chip integration, the device offers a potential solution for all-optical signal processing in photonic integration circuits.