Typically sliders and galleries want at least one dimension to stay constant. Otherwise it is very difficult to anticipate usage because the gallery could contain images from the size of a thumbnail through to a giant HD wallpaper. That would break most websites layouts. Scaling the images to the longest dimension allows to some consistency to be given. Alternatively lightboxes are used where the dimensions are less important and the image is sized in relation to both the original, or if it is a large image - to the maximum that is viewable on the visitors screen.
You would open up many more possibilities of doing this easily if you ran your images through an automated process to generate consistent images, or allowed Wordpress to do that for you by setting a desired size. What you are asking for is an uncommon usage of a slider.
The image height would be the same but the widths would be different.
I would also like the thumbnails to have the same height but different widths but I could deal with thumbnails that have the same widths and height.
Most of the wordpress plugins I have seen that look like they could do this say the slideshow must be a set width and height. This seems crazy, I wanted to use this for a photography portfolio and I don't want to crop the images to fit a slideshow.
Do you know of a plugin that has the sort of use I need?
Do you mind using the lightbox style or are you wanting to display it in a page? Really the only limitation is how much space you have to play with and how you want to present the gallery/slideshow.
If you use a lightbox slideshow then it is easy to have both thumbnails and images display on screen and size it so that it will show each image as big as possible. Alternatively if it is bigger than the screen will allow it will scale itself down. This is the easiest way to get all photos to display with a mix of odd sizes or shapes. The computer is sizing them to fit the screen.
If you want to insert a gallery into a page, chances are that you are already limiting some part of the images. If in your case you are limiting the height, you will likely find that all your images are pretty close horizontally. One thing to note is that although the sliders ask for dimensions, the images themselves DON'T have to be these exact dimensions. So for arguments sake you have 10 images and they all have different heights and widths. When you insert your Slider it asks for dimensions. That is the maximum dimension any image will be able to fill. You can choose whether each image will scale up or down or stretch to fill the display space. This means you don't have to worry if your image is smaller or larger than the area, the slider will make sure it fits.
This means in practice you don't have to have images that are all uniform on either height or width.
So it is a matter of presentation style. Do you want to show the photos in the context of a page, or dim the lights and let your users screen be totally covered in images.
All this to say you have lots of choice, it will just be implemented slightly differently.