Anh, I was in your situation a number of years ago. I was able to go into Canada and back on simply a green card with no problem... Same with Mexico. Of course, both times, I drove, so it wasn't a problem. You might want to check at a site like http://travel.state.gov
- you may be able to go to US territories (i.e. PR
, Virgin Islands, Guam) without any issue as long as it's a direct trip. As for going to other countries, while being a permanent resident will grant you re-entry to the US, you may not be let into others w/o an actual passport.
Do you have proof of entry into the US from Vietnam? All my Vietnamese friends were granted US citizenship almsot instantly due to refugee status, well after the war. You might want to look into that before relations thaw up to the point that you're in limbo! If that's not an option, look into charitable organizations that have citizenship services. I applied through Catholic Charities, and since they put so many applicants through en masse, I had the whole process done in less than a year.