Before starting the oracle installation give xhost+
Afer that try this xclock it should show you the clock
Your quoted messages look pretty self-explanatory. Which of those detailed steps are you having difficulty with?
A little background ...
The OUI (and a few other oracle utilities) are GUI applications. On *nix, that means they are x-windows (x-11) apps. As such, they require an x-windows server be running on the machine that is actually controlling the display. The typical *nix server setup is that you connect to the server from your desktop using an ssh client, such as putty. You also have an x-windows server running on your desktop. There are several products available for this. Exceed is one popular (and expensive) product that includes the x-server among several other functions. I use xming because it is free, lightweight and does only the one thing I want -- x-windows service). After connecting to the db server, you need to tell the os where to send the x-11 output. Historically that is done by setting the DISPLAY variable to the ip address and display number of the machine that is supposed to receive the output. There are other methods that can be preferable, especially since your desktop is probably DHCP and you'd have to check the IP address every time. I prefer to set my putty session to use x-11 port forwarding. With that I don't have to do anything special on the *nix server -- no DISPLAY, no +xhost. Just make sure xming is running on my desktop, connect and go.
As has already pointed out, this won't work if you log on as someone else (say, root) then su to oracle. You have to log on directly as the user that will be using the x-11.
BTW, it would be really helpful if you would go to your profile and give yourself a recognizable name. It doesn't have to be your real name, just something that looks like a real name. Who says my name is really Ed Stevens? But at least when people see that on a message they have a known identity. Unlike the system generated name of 'ed0f625b-6857-4956-9b66-da280b7cf3a2', which is like going to the pub with a bag over your head.