External Human-Machine Interfaces (eHMIs) have been proposed to facilitate communication between Automated Vehicles (AVs) and pedestrians. However, no attention was given to Deaf and Hard-of-Hearing (DHH) people. We conducted a formative study through focus groups with 6 DHH people and 6 key stakeholders (including researchers, assistive technologists, and automotive interface designers) to compare proposed eHMIs and extract key design requirements. Subsequently, we investigated the effects of visual and auditory eHMI in a virtual reality user study with 32 participants (16 DHH). Results from our scenario suggesting that (1) DHH participants spent more time looking at the AV; (2) both visual and auditory eHMIs enhanced trust, usefulness, and perceived safety; and (3) only visual eHMIs reduced the time to step into the road, time looking at the AV, gaze time, and percentage looking at active visual eHMI components. Lastly, we provided five practical implications for making eHMI inclusive of DHH people.