I don't know of any programs for the PSP that will do soft subs, but I can give links to a free encoder and tutorial with links to create a video with hard subs.
How to add permanent subtitle to a video with virtualdubmod - VideoHelp.com PSP Video 9
After you follow the tutorial to add hard subs run it through Video 9 and you should have subtitled video capable of being played on your PSP.
Edit: You might have to play around with the font size (probably make it bigger) for the subtitles in VobSub so they're still readable after being converted to the PSP.
You'll probably have encode twice unless Video 9 can be made to accept it's input video directly from avisynth. The good news ia the PSP'a screen is relatively small so any compression artifacts from encoding twice shouldn't be as noticeable.