1. Is your external USB hard drive a USB 3.0 or not? If it is, I don't think Easeus linux bootable disk has USB 3.0 drivers, only 2.0 and 1.1.
2. Also, try to connect the USB drive to your computer while it is off and then boot with the bootable disk.
3. Creating a Easeus WinPE bootable disk rather than the default linux bootable disk may also resolve your issue. Most of the bootable disks from backup/recovery vendors are linux based by default and may give an option for WinPE based bootable disk.
4. There's also the possibility of looking at BIOS settings regarding the USB interface.
The tool I use give both for an option and even a DOS based one with USB drivers. Not free but reasonable from Terabyte Unlimited: Image for DOS ($30), Image for Linux($30), Image for Windows ($39 but you are also licensed to DL and use the DOS and Linux version; so it's 3 in 1). The title of DOS and Linux is sort of a misnomer, it does not mean the operating system you are trying to image , but it is the nature of the bootable disk it creates. The Image for Windows version is that it is installed on Windows and can do live imaging while Windows is running, while the DOS and Linux version are run from bootable USB or disks.
For free give these a look:
Macrium Reflect ( http://www.macrium.com/reflectfree.aspx
DriveImage XML ( www.runtime.org/driveimage-xml.htm
) free a try.
Also there is Redo Backup which imaging and restore are both from the bootable linux cd. http://redobackup.org