How do I check external USB Drive health?

Another alternative would be CrystalDiskInfo You can download the portable version so you can test without installing.

Most tools have trouble passing the SMART status of hard drives over USB.

Your best bet for getting the health status from the drive over USB from a generic tool is smartctl from smartmontools. A version that works on Windows with a nice GUI is available here. If this does not work, you will have to download and install the device specific management tool from the manufacturer. The management tool will have a health checker for the drive. Here is the site for western digital. Here is the site for Seagate. You could also take out the drive from the external enclosure and hook it up to your PC directly using SATA or IDE and then read the status using standard tools like HDTune or Smartctl.

smartctl support for USB is described in more detail here.

Give HDDScan a try. It does SMART value reporting from ATA/SATA/USB/FireWire and analyzes log pages from SCSI drives. It can also perform SMART tests on hard drives connected by any of the above-mentioned interfaces.