Insect-scale micro-aerial vehicles, especially lightweight, flapping-wing robots, are becoming increasingly important for safe motion sensing in spatially constrained environments such as living spaces. However, yaw control using flapping wings is fundamentally more difficult than using rotating wings. In this study, an insect-scale, tailless robot with four paired tilted flapping wings (weighing 1.52 g) was fabricated to enable simultaneous control of four states, including yaw angle. The controllability Gramian was derived to quantify the controllability of the fabricated configuration and to evaluate the effects of the tilted-wing geometry on other control axes. This robot benefits from the simplicity of directly driven piezoelectric actuators without transmission, and lift control is achieved simply by changing the voltage amplitude. However, misalignment or modeling errors in lift force can cause offsets. Therefore, an adaptive controller was designed to compensate for such offsets. Numerical experiments confirm that the proposed controller outperforms a conventional linear quadratic integral controller under unknown offset conditions. Finally, in a tethered and controlled flight experiment, yaw drift was suppressed by combining the tilted-wing arrangement with the proposed controller.