Easy and efficient way to run GNU/Linux on top of Android on an x86 device?

I found way to do this that I'm very happy with.

I used Linux Deploy. (It requires root, but here's an alternative for those who don't want to root.)

Here's a nearly full version of Xubuntu 16.04 (x86-64) running on my phone.

It performs really well. I had no performance issues. Note that this is not a virtual machine. Android and Xubuntu share the very same Linux kernel at the same time. If, while this is running, I switch to OS monitor (in Android), I can actually see the individual processes from Xubuntu (dpkg, etc.) running and how much of the CPU they're using. (That has to be enabled in a setting, though.)

An external keyboard and mouse are a must (though not strictly required). And an external monitor is also a good idea. Or you can just VNC into this system directly from another computer. Linux Deploy supports that out of the box.

The setup is really easy. The default settings of Linux Deploy pretty much work. Just select your distribution and desktop environment. But, by default, the system creates a 2GB .img file as a file system. That wasn't enough for me. So since the internal storage of my phone is ext4 formatted, I was able to set it to 40 GB. If yours is FAT32, the maximum will be 4GB. But it's also possible to have a directory or partition instead of a .img file. (Although I didn't figure out how to do that.)

The process is described in detail here. Skip down to the "Linux Deploy" section. It's important that you install the correct version of Busy Box. Otherwise, it won't work.

This kind of thing has potential. If you have a powerful enough phone, it can actually replace your desktop computer in many cases.