I just got my Roku box the other day so bear with me, but I believe I have a working solution.
I have a Roku 2 XS with the newest firmware. I've been working with an MKV I downloaded of A Good Day To Die Hard. There is a Russian sequence in the first 2 minutes of the movie. I used Handbrake to convert the movie to MP4. I imported the SRT file into Handbrake when I converted and, although Plex shows it in the Playback Options menu for the individual movie, selecting it does not display subtitles no matter what.
However, I edited the SRT with Notepad and found that it had a blank line at the top and two at the bottom. I removed the blank line from the top and left only one blank line at the bottom. I named the file the same as the movie and left it in the same folder with the MP4.
In the Playback Options menu, I selected Unknown (SRT) for the subtitles. (The one I imported into the MP4 was still listed as English () )
When I selected "Soft" in the Plex options under Subtitles, The subtitles are displayed as small yellow lettering.
When I select "Burned in" the subtitles are white with a black edge and slightly larger than the yellow ones.
I have enabled on the Sever Settings > Agents > Movies > Personal Media > Local Media Assets (Movies)
The subtitles display consistently in the Direct Play and Automatic playback modes.
What I have not yet done is re-converted the MKV to MP4 with Handbrake using the new, edited SRT file. I'll update in the next few days.
I've been trying multiple movie formats the last few days to find the right balance between quality and reliability. I've used the settings from Rokode for a 720p file in an MP4 container with AC3 Passthru for audio. Maybe it's my network but 1080p movies seem to have trouble with buffering. I have a 60in LED TV and I can't tell a real difference between 1080p and 720p on streaming video anyway.
I have a DTS receiver, but I chose AC3 so I could use the MP4 container for broader compatibility. Roku/Plex only does DTS passthru with MKV