We propose a dynamic scheme to realize mode-switchable generation of LP11a/b modes and ±1-order orbital angular momentum (OAM) modes simultaneously, which are induced by an acoustically induced fiber grating driven by radio frequency modulation. LP11a/b mode degeneration in a few-mode fiber is induced by the geometric irregularity of optical fibers. A dual-wavelength resonance of mode coupling from LP01 to LP11a/b modes is found based on the combined effects of optical and acoustic birefringence. Within the configuration of continuous-wave intra-cavity laser output, we experimentally demonstrate a fast-switchable generation of LP11a/b modes and optical vortex beams with ±1-order OAM at a switching speed up to 4.3 kHz. This approach has potential applications in mode-division multiplexing, particle manipulation, stimulated emission depletion microscopy, and quantum information science.