I ran OpenWRT on my Eee701 (mostly to test Node.js). A few notes…
Use the combined image: openwrt-15.05-x86-generic-combined-ext4.img.gz
Unpack it. Write it to a USB drive with dd. For me, it boots my Eee without any modification.
Networking
You probably want networking.
Download: kmod-atl2_3.18.20-1_x86.ipk.
I suggest you put it in /root on the filesystem of the above mentioned image, before starting up.
As with the RPi, you might want to edit your /etc/config/network to act like a pure client on the network:
config interface 'lan' option ifname 'eth0' option proto 'dhcp' option macaddr 'XX:XX:XX:XX:XX:XX' option hostname 'rpiopenwrt'
USB Storage
It seems you need to install usb-block-support the usual way… and then it is good to have network.
Have you by any chance tried installing OpenWrt on a D-Link DWR-116 router?
No, not tried on DWR-116, and I doubt it works: http://wiki.openwrt.org/toh/hwdata/d-link/d-link_dwr-116_a1
It seems similar to the Archer C20i though, which I have tried.