I'm not sure about openwrt, but I use Mikrotik/Routerboard products, and I can use either protocol. I connect the Arduino to the usb port on the Routerboard (gets power there too), and the ethernet shield to one of the ethernet ports. I can ssh into the router and connect to the Arduino usb like a serial monitor, or use the ip address with TCP/IP as either a server or client.Maybe openwrt has that usb feature also.
Taht depends o what Hardware the openwrt is running.For example a little TP-Link WR703n pocket router has a USB port that is usually meant to receive a USB 3G Modem. Running openwrt that USB port can be repurposed to connect and communicate directly with an Arduino.I don't have any direct experience with that.The more common way is to connect the router per Ethernet and TCP/IP to an Ethernet Shield/Arduino.
I am not sure what you mean with "conversion" so here is a link to the openwrt site with this routers info.http://wiki.openwrt.org/toh/tp-link/tl-wr703nBase on a previous thread her in the Networking section of the forum I know that there are users that have successfully connected said router per USB directly to an Arduino.