I was never much into math until after I left university and now I am constantly kicking myself for not finding the small little subfields of math that I now find useful and interesting. You can get a long way in stats with a pretty basic understanding of how it all works; a lot of what you might do here is the sort of stuff that you can pull out of intro stats books -- you are not going to be writing the stat anaysis code, you just need to know when and how to apply it. You would probably also be well-served by learning a bit about visualization and how to present quantitative information to a lay audience.
Do not aim for a side-project that will be universally useful to all NGOs or even to one NGO, aim for a side-project that someone in a position of authority will think is cool or which can serve some small facet of the organization. Think mashup or something small like a heatmap that shows where most of the volunteers/donors live, etc. Don't solve their big problem as your side-project, solve some small problem that can be used to show them that you are capable of solving the big problem (if they hired you to do that task, for example.)