I haven't tested it but I found a code example in the Arduino IDE for Galileo, under Examples>USBHost>MouseController. It might be helpful for you.
I also found the following thread: How to connect Intel Galileo to PC as USB HID where there is a discussion about using the Galileo board with a mouse or keyboard. According to the discussion, it is possible but you will need the drivers and enable some options during the kernel building.
I also found these two threads where there are some discussions about using the USB feature. I hope you find them useful:
- Reading USB Host events using Arduino IDE
- Re: Galileo as Host for USB-To-UART-Adapter not working (ODROID-SHOW Display)