This paper is concerned with the robust guidance and control of fully actuated multirotor aerial vehicles in the presence of moving obstacles, linear velocity constraints, and matched model uncertainties and disturbances. We address this problem by adopting a standard hierarchical flight control architecture consisting of a supervisory outer-loop guidance module and an inner-loop stabilizing control one. The position and attitude control laws are designed using a proportional-derivative approach combined with a sliding mode disturbance observer. On the other hand, to design the guidance, we propose a robust version of the continuous-control-obstacles method, which derives from the velocity obstacles one, to drive the vehicle to a target pose while avoiding collision with moving obstacles and violation of linear velocity constraints. The overall method have been numerically evaluated and shown to be effective in providing satisfactory tracking performance, collision-free guidance, and satisfaction of linear velocity constraints.