In this paper, an algorithm for robust adaptive control design for parametric-strict output feedback switched systems is developed. Under extensions of typical adaptive control assumptions, the control scheme guarantees system stability for bounded disturbances and parameters without requiring a priori knowledge on such parameters or disturbances. The problem reduces to an analysis of an exponentially stable and input-to-state stable system driven by piecewise continuous and impulsive inputs due to plant parameter switching and variation. This system is a modification of the closed loop error dynamics in standard adaptive control systems, through a generalized leakage-type adaptive controller. The results are illustrated via simulations and compared to other adaptive and non-adaptive control methods.