I think the other commenters have addressed the issue of "giving food the homeless" here, but as far as sending them to other countries...
Conveniently enough, I found a guide to orange carton dimensions and weights: http://www.south-africa-fruits.com/citrus-packaging.html
So, let's see how much it costs to ship a carton of oranges from, say, Florida to Kenya (they could definitely use some citrus)! Oranges, while a pretty hardy fruit, have a shelf life of, at most, a few weeks at room temperature, according to multiple sources. I don't know if they'd be great sitting around in a cargo ship, with uncertain temperature and humidity changes for a month. So let's fly them over. Here's a calculator: http://www.worldfreightrates.com/en/freight
I calculated $154.74 - $171.02 per carton. That's quite a hefty premium on a carton of oranges (about 100 oranges, according to multiple sources). Sure, you might argue that a benevolent organization could come along and send bulk pallets (unfortunately, I couldn't find anything that would let me calculate the costs for a pallet of oranges), but I doubt you're going to find more than a 20% costs savings -- competition in this industry is stiff, and jet fuel is expensive.
In Boston, can buy navel oranges at my local grocery store for a dollar an orange, or less (I just checked Peapod!). So, yeah, it literally costs more to ship an orange across the ocean than oranges here cost, even with the relatively high cost of labor in the US. As wealthy Americans, we frequently pay for exotic foods (bananas in the middle of winter!) that cost very little to produce, and we're paying almost entirely for shipping. We don't think much about shipping costs, or think that it's unusual to get our food shipped to us, but that sort of thinking is dangerous.
It's far far cheaper to grow more food in starving countries than it is to ship them food. In Kenya, and all over Africa, food prices are much cheaper than they are here, even on open markets with relatively inefficient food delivery practices. It is cheaper (not to mention more environmentally sound!) to produce the food there, than it is to produce it here, and then transport it there. You make no sense. I mean, people in many African countries (let's be honest, Kenya is one of the wealthier ones) commonly feed their entire families on just a few dollars a day -- why not compost the fucking oranges, send them the money we would have spent on spilling fuel into the atmosphere, invigorate their economy, and let them eat like kings for the cost of flying over three oranges?
Saying "Now I understand there would be a cost in transporting these goods, as well as other factors, but still..." is just irresponsible. Yes, seeing oranges go to waste makes you feel bad. But the solution is not to ship it outside the relatively small radius where it makes environmental and economic sense to do so, when there are many other solutions for hunger that don't waste resources and kill the environment faster.