ListDisks Operation will give you all the Azure Disks that are present in your account.
The result set contains objects with properties like AttachedTo
which you can use to identify a VM (if any) to which this disk is attached, or SourceImageName
which you can use to identify the source image.
There is no direct API call to identify which images are in use. You have to make two calls - first one to get all disks and second one get all images. Then mix and match. (Or try out filtering the images only based on names, which you are interested in, but I am not sure whether the REST API supports filtering).