I have an Xperia X8 phone, and I'd like to know if I can install a non-Android Linux OS on it? I would like to have a light Linux Distro, like Kolibri or something like that.
There are two ways to get a custom Linux running on an embedded device, in general:
Search the web for projects describing how to port some distro to exeactly the device in question. If you find it and it looks well described, you're a happy person :) My tip here: Look at success stories first! See what actually can be done (what final functionality did people get).
Advanced: use generic porting procedures, such as described here. You will need to do a research on your own, to find out what peripherals are supported, where and how to get drivers for them etc. One thing's for certain: You will need to build custom kernel for that and most often it will include getting a specific kernel version and a lot of patching. In many situations, there might be a high risk of bricking your device involved.
Always remember that in majority of cases at least some parts of the hardware will not be (yet) supported. Always have a close look at what's achievable before you start.
One might also take a different approach to the "Advanced" option, specifically in the case of Android-based devices: Since the given device runs a Linux-like kernel, you can use it with all the ready modules etc. But then you'll have to adapt the standard Linux userspace programs to play nicely with the not-really-linux core.