If you don't need a desktop environment, you could use a minimal Debian image as a starting point. It boots to the login prompt unless you configure it to do something else (see below). However, if you want to stick to an Ubuntu version that's unmaintained as of this month, I guess it's enough to disable the upstart script for the display manager - not sure which one was used back then.
In order to "switch off the internet service", well, maybe you should be more specific. Do you want LAN access? If you don't, pull out the cable
However, if you need LAN access, there are several ways of achieving that goal. It's also a question of security needs. A simple local hack would be to configure ethernet settings manually in /etc/network/interfaces without setting a gateway. Your odroid will "know" the local subnet, but it won't "know" how to leave it. However, anyone with physical access to your device could change that by simply taking out the sd-card/emmc for editing those settings on another computer. I guess it's better to block internet access for the odroid on your local router.
Starting an executable file automatically can be done in various ways - for example:
- create a systemd job - or, on Ubuntu 14.04, I guess it should be an upstart job
- write a tradional init script
- start your executable via /etc/rc.local
I'm aware this isn't a full how-to, but I hope I've provided some clues that help you research a solution that fits your needs.
Edit: If you want to prevent any network access and not providing an ethernet cable isn't secure enough, you could:
a) compile your own kernel without support for the c1's network
b) spend $28 on an Odroid C0
- it doesn't have an RJ45 socket.