For this Tutorial, there are some Assumptions:

1. You can format your usb drive (did you do a backup?)
2. Your USB drive is the /dev/sdb device (You can check yours with sudo fdisk -l or using Gparted)
3. Your USB drive will be mounted at /mnt
4. You are using a Ubuntu distro (any Ubuntu flavour) - Could be a live session (LiveCD)
5. You are logged with the first user (seated at installation or live session default)

To create a EFI firmware compatible boot drive, you need a GPT partition table and at least one FAT32 partition. Do as follows…

sudo apt-get install gdisk
sudo sgdisk --zap-all /dev/sdb

You probably need to remove and insert the USB drive again at this point for the kernel to update information about it…

sudo sgdisk --new=1:0:0 --typecode=1:ef00 /dev/sdb
sudo mkfs.vfat -F32 -n GRUB2EFI /dev/sdb1

We are done with Step One, you can check modifications with sudo parted -l or with Gparted.

Mount the usb drive…

sudo mount -t vfat /dev/sdb1 /mnt -o uid=1000,gid=1000,umask=022

To make life easier, I created a pack with all necessary files for you to modify as you need. If you don't trust my files, create yours using this page as reference. Link to Download is: http://webativo.com/uploads/files/usb-pack_efi.zip.

Extract the zip file and paste those inner files using Command Line Interface or a file manager you like.

cd ~/Downloads/
unzip usb-pack_efi.zip
rsync -auv usb-pack_efi/ /mnt

The most important files are bootia32.efi to boot on 32bit machines, bootx64.efi to boot on 64bit machines and grub.cfg to setup grub to load ISOs or chainload to other paths.

In the end, you might get a directory tree like this:

/usb_grub2_drive/
|
|- boot
|   |
|   - grub
|      |
|      - fonts
|      - grub.cfg
|      - grubenv
|      - i386-pc
|      - locale
|      - menu.lst
|
|- EFI
|   |
|   - boot
|      |
|      - bootia32.efi
|      - bootx64.efi
|
|- iso
    | 
    - android-x86-4.4-r2.iso
    - linuxmint-17.1-cinnamon-64bit.iso
    - lubuntu-15.04-desktop-amd64.iso

sudo grub-install --removable --boot-directory=/mnt/boot --efi-directory=/mnt/EFI/BOOT /dev/sdb

PS: Grub2 installation might throw some error messages, just ignore it. PS: If you have problems to copy and paste content on /mnt, you can use sudo to do it

Put (copy) the .iso files you want to load in /mnt/iso/ and setup grub.cfg like the existing examples…

Note that the most important variable to set is isofile. There is lots of examples on the web about how to configure grub2 menu. Use # to comment those lines you don't want to use, e.g. to hide a configuration of absent .iso at /iso.

First and most important, deactivate secure boot on your computer's firmware. Search on the web if you don't know how.

To boot the USB drive you can set your machine firmware to search first for the USB device (boot order). Or you can choose what drive to boot as soon as you turn on your computer. Each manufacturer has its own keys to do it. Search for your machine's manual if needed.