You may refer to this step by step guide to hardcode subtitles at Convert Soft Subs to Hard Subs to Hardcode Subtitles to MP4, AVI, MKV
It applies to:
Here is no way for an external SRT to work with a xbox. The subs need to be burned as part of the video. Handbrake can add hard subtitles to videos and here is the way to do that: http://www.videoconverterfactory.com/tips/handbrake-subtitles.html. Yet you can't remove this subtitles anymore.