I haven't used SOIL, but just looking at the header file's documentation gives you nice information. Have you tried something like this:

int width;
int height
int channels;

// Loads the image and gets its width, height and the number of channels
unsigned char *data = SOIL_load_image("kewltexture.png", &width, &height, &channels, SOIL_LOAD_AUTO);

// Generates a texture from the data you've just loaded
unsigned int textureid = SOIL_create_OGL_texture(
	data,
	width, height, channels,
	SOIL_CREATE_NEW_ID,
	SOIL_FLAG_MIPMAPS | SOIL_FLAG_INVERT_Y | SOIL_FLAG_COMPRESS_TO_DXT
);

// And remember to free the image data
SOIL_free_image_data(data);

If you have the GLuint texture object, you can glBindTexture it and issue some glGet* calls.

glGetTexLevelParameter: http://www.opengl.org/sdk/docs/man/xhtml/glGetTexLevelParameter.xml - for height and width.

glGetTexImage: http://www.opengl.org/sdk/docs/man/xhtml/glGetTexImage.xml - for data.

In the latter case, I hope you're not intending a usage similar to LockRect/Map in D3D; OpenGL doesn't have API calls for this, so instead you'd use a PBO or retain a copy of the texture data in system memory.