Without knowing your location, it's hard to give accurate information, so I'll speak to the U.S.:
You own the copyright to any photo for which you mashed the shutter button. You can license those photos in a variety of ways: To whomever, for whatever usage, for whatever duration, in exchange for whatever compensation. As a general rule, you don't transfer copyright to anyone (though you can do so if you wish).
In your specific instance, you'll retain the copyright, and you'll grant a license to the organization do use the images in whatever manner you wish to allow. You can choose to require them to give you photo credits and/or leave your watermark on the images; you can choose to allow or disallow them to put their own logo or watermark on the images.
You also retain the rights to use the images in your portfolio (with or without their logo); however, if there are any identifiable people in the images, then you'll want to get a model release. The model release allows you to use those people's likeness for "business purposes," and a professional portfolio may fall under the heading of business-related usage. If you're on good terms with the organization - and I'm sure you are, if you're volunteering with them - then they'll likely give you a model release without any hassle.
If you're just putting the images on a personal (not business) website, for a non-professional portfolio, then I don't believe you have to have a model release. It's nice to ask permission first, of course.