I have a weird looking jack : http://imgur.com/lDbYNmb, is this jack campable of being converted to ethernet?
This is a phone socket. You could wire a plug to a normal Ethernet cable and arrange for three of the four signal pairs to work through the plug/socket pair. However, you would have to make similar changes and replace whatever cable is behind that socket with an Ethernet cable. Normal phone cables are not practical for carrying Ethernet signals.
Also, if you did use the correct cable type to the plug and the socket, it would work only for 10/100 MHz Ethernet. 1 GHz Ethernet requires for pairs, but the socket only has enough pins for 3 pairs.
In practical terms, by the time you have replaced the wiring behind the socket, you will find the answer is NO.
That's a standard UK telephone socket.
You can't 'convert it' to ethernet, although if you sign-up for broadband you can use a micro-filter to connect your router to it.
You, probably not. Me, no problem.
What matters is the cable, and what is connected to the far end of the cable.