VLC stops streaming at the end of the file (or playlist, if set up correctly), so by the time you get to work, the movie is over and the stream stops.
VoD solves this problem. VoD is Video on Demand, and the way it works is as follows (roughly):
1. VoD objects are set up through telnet or http interface.
2. Client machine accesses them like a stream (with some add'l stuff).
3. VLC starts playback of file used as VoD object and streams it to client.
Basically, VoD is like having a stream that doesn't start until you try to open it.
As for protocols, I would suggest UDP, as most corporate firewalls don't have a problem with this, but they do with HTTP.
To learn how to set up VoD objects, see the Streaming How-to.
Also, you need to use your external IP address, not your internal network one. To get this, go to
http://www.lawrencegoetz.com/programs/ipinfo/ or someplace similar from your home machine. Take this IP address to work and ping it using the command prompt (Start > Run > "cmd" > "ping ip_address"). If it says "Destination host unreachable", you may be stuck unless you have a pal in IT who can allow that traffic through for you. To find out what TTL setting you need, run "tracert ip_address" in the command prompt. It will list all the routers it crossed. Take that number of routers, add 2 or 3 (to be sure), and set that as your TTL at home.