You could run Kodi, Emby, or Plex and get local access through DLNA access.
I have a QNAP RAID set up that Emby catalogs and handles access for. An Emby app on my LG TV, and a Roku on other TVs. Some RAID systems will just plug into your network and allow you to install apps on them directly.
Another option is to use MediaMonkey to catalog and provide access. They even have an Android app.
Lastly, regular external HDD are meant for occasional access, not continuous work. Most have a duty cycle of about 25%, meaning they should only be run about that amount of time before dying. This is why I went with NAS HDDs. If you have the money, go with an expandable RAID. Once you start using that capacity, you'll find you want more.