photorec, despite its name, can be used to recover all sorts of files from a reformatted drive, including documents, photos, movies, etc. You may have better luck than normal because the format wasn't complete.
You'll need to have a different drive with at least as much free space as what you had used in your formatted drive in order to store the recovered files. It also may take some time piecing together different parts of files due to fragmentation of the formatted drive. Either way it's a good first step as it will recover a lot and won't make things worse for your formatted drive.
testdisk comes from the same family as
photorec, but may offer tools to rebuild your disk's partition information and file structure without having to recover byte by byte. Many of these operations will write to the disk, so it's best to perform them on an image of the disk. You can create one using
dd. This image will be an exact copy of the USB drive in its current state, including its MBR, partition layout, filesystem metadata, filenames, directory structure, as well as the values of all of the bytes on the disk. Of course, not all of this information is available on your USB disk anymore.
dd command would be
dd if=/dev/sdc of=path/to/image.img
Make sure you know the device node of your USB drive (
/dev/sdc in this example). You can find out by using
fdisk -l (as root) or by looking in the directories under
/dev/disk/. Also, the size of the output file with be the same as the USB drive so make sure you're placing it somewhere that has enough space.