Aerial robots have garnered significant attention due to their potential applications in various industries, such as inspection, search and rescue, and drone delivery. However, the ability of these robots to effectively grasp and land on objects or surfaces is often crucial for the successful completion of missions. This paper presents a novel modular soft gripper design tailored explicitly for aerial grasping and landing operations. The proposed modular pneumatic soft gripper incorporates a feed-forward proportional controller to regulate pressure, enabling compliant gripping capabilities. The modular connectors of the soft fingers offer two configurations of the 4-finger soft gripper, H-base and X-base, allowing adaptability to different target objects. Furthermore, when deflated, the gripper can function as a soft landing gear, reducing the weight and complexity of aerial manipulation control and enhancing flight efficiency. We demonstrate the efficacy of indoor aerial grasping and achieve a maximum payload of 217 g for the proposed soft aerial vehicle (SAV), with the weight of the soft drone being 808 g.