A lot of that is going to depend on your skills. Unfortunately, though, the bottom line is that for virtually all types of jobs, countries want their own citizens to have the first crack at them. As an expat, unless you have particular skills that cannot be provided by a local citizen, it is going to be a tough door to open.
Being a native English speaker is a skill that is in short supply in most Asian countries, hence the readily available job market for English teachers. However, if you look at other career paths, IT, Business, etc. there are plenty of willing and able locals that are well educated, speak the language and are willing to work for far less pay and benefits than an expat.
The primary deviation from this are multi-national companies HQ'd in the west that like to keep a complement of western managers on-hand in their various global operations. To get one of those jobs, however, you generally work in the home country for awhile first, before you could be eleigible for an overseas package, which can in many cases be quite lucrative from a comp and benefits perspective.
Many volunteer programs I am aware of actually require you to pay a fee to volunteer to cover your own housing and meals and a lot of them have people lining up to do it, so I am not sure there will be much there either. Again, though, what your skills and education consist of will have a lot to do with your options.
Not trying to be negative, but it is going to be a hard road. This is not to say its impossible, but it is difficult and there are many, many expats looking for work in Asia. If you really want to do this, you will have to put in a lot of time and really try to identify a niche for yourself. The best thing you could do is start networking with other expats in your area. Talk to them, figure out what the heck they are doing in Asia, how they got there. See if they have any advice or ideas. At the end of the day its a lot like job-hunting in the west. It often comes down to who you know (and actually, that is 10 fold more important in Asia). Good luck.