In post #6 you say the Edimax dongle is using a Realtek RTL8188CUS chipset. The log is showing something a little different (though it might not be correct):
[ 5.641316] CHIP TYPE: RTL8188C_8192C
And OSMC has loaded:
[ 5.641005] rtl8192cu driver version=v4.0.2_9000.20130911
According to this post, the EW-7811UN should work. Are you using an official power supply?