If you want, say, money to go to disease eradication in Africa, voting in the US doesn't help much for that, but donating to private charity does.

Maybe not, see Carl's comments here and here.

I'd speculate that it's more efficient to give to advocacy groups than to vote for politicians, because an advocacy group can develop long-term strategies and use the court system. If you're mainly concerned about a few issues, especially if they're not in the political mainstream, advocacy groups seem intuitively like a much better bet.

This may very well be true and some of my friends have a similar intuition. I'm interested in learning more about this matter.