While I don't agree with tomas123's attitude, the answer is and has been given numerous time on this site.
The easiest way to do this, since your hypothetical scenario includes being outside of your network would be to use ftp to share your files and use an audio player that can stream with that protocol.
The real question is going to be can your home bandwidth connection handle it. I think audio would be fine if you are on at least a cable/dsl connection but video is a bit doubtful. Unless you have a fat pipe with high upload speed, video just will not be possible (at least good quality video). Just do yourself a favor and get a PDA, ZUNE, IPOD, etc and just load it up with what you want to watch and take it with you.