(I apologize if you're not using Windows, since this is how I wrote this 'guide')

Use mkvtoolnix to extract the sub files, then use a program like VirtualDub to 'burn' the subtitles onto the actual video file. From there, you can convert the file to the PSP's format.

mkvtoolnix
(Download the installer, because I believe a GUI version comes with it)

VirtualDubMod
(Download and extract to your desktop)

1. Run mkvmergeGUI from your start menu
2. Click on 'add' next to the 'Input Files' text box and choose your file
3. In the 'Tracks, chapters and tags' box uncheck everything except for the subtitle stream.
4. Click on 'Browse' next to the 'Output filename' box to select where to store your subtitle file
5. Click 'Start muxing' to save the subtitle
6. Follow this guide to 'burn' the subs.