First, what makes you assume that all those donations are intended to help the poor? No doubt some are, but most are intended to defray the expenses of spreading the Gospel, the "Great Commission" Jesus left for us. Religious people do not have to apologize for their efforts to help those in need. They did a heck of a lot more and sooner than government in helping disaster victims, for example those affected by Katrina.
Second, why do you single out religion but let governments and the UN off the hook? The problems you identify are not ones created by lack of money, not considering the trillions the developed world has pissed away on foreign aid. Rather, they are problems of corruption, waste, fraud, misplaced priorities, socialism, communism, war, etc.
An eternal question faced by religion is why does God allow tragedies to take place? Some will say the victims brought it on themselves by sin or lack of belief, others will say that God gives us free will and what we do with it is our problem, others will throw up their hands and say we can't be expected to understand His ways or why He does or doesn't do something.
