Ziatron: I recently upgraded to El Capitan, and I just ran into the same issue with a Verbatim 16gb 'STORE N GO' USB drive, which I wanted to encrypt. The Disk Utility gui showed no partion on drive, and there was no partitioning option available in the gui (partition button was greyed out). So I erased it using the gui; and formatted it as OS X Extended (Journaled). There was no option to erase it and reformat it as OS X Extended (Journaled) Encrypted. After the USB drive was erased, no partition was shown in the gui. I checked the USB drive using the diskutil 'list' command, and it showed no partitioning. So I then erased the USB drive using the diskutil 'eraseDrive' command, formatting it as JHFS+. I checked the USB drive with diskutil, and it showed that it had been partitioned. Then I checked it with the gui, for ha-ha's, and found that the USB drive still did not show any partitioning. I was able to encrypt the drive by selecting it in a Finder window, and right-clicking on it. Finder did not show a partition to encrypt. I selected the drive itself.
To summarize:
1) Erase the USB with the Disk Utility gui, setting the format as OS X Journaled.
2) Erase the USB using the diskutil 'eraseDisk' command.
i.e., diskutil eraseDisk JHFS+ STORENGO disk3
3) Select the whole disk in a Finder window, right click on it, and then select 'encrypt'.
It may be possible to combine steps 1 & 2 into 1 step, by only issuing the diskutil command. However, I did not have the opportunity to test that.