Some models can be reflashed with stock Linux using various poorly documented and largely forgotten tools; the Linux distribution is here:
http://the.earth.li/pub/e3/ and there's some writeup on it here:
https://www.earth.li/~noodles/hardware-e3.html
The downside is that that Linux distribution is actually built with OpenEmbedded and won't run binaries built anywhere else, which is irritating. I have successfully run Debian on an E3 via a USB hub with a hard drive attached by simply cross-installing the userland from a PC and then configuring u-boot on the emailer to boot from it. However the emailer's only got 32MB of RAM so whatever you do it's going to have to be very lightweight. Finding a sufficiently old userland might be hard, too --- it'll need to work with a 2.6.19 kernel.
Also, Amstrad eventually locked down the bootloader and later versions can't be flashed. If you have one of those, you may be out of luck.
You'll also need to build a serial cable. The signals are TTL 5V, except inverted, so 0V = logic 1 and 5V = logic 0 (it's intended to be passed directly to a level shifter).
The best thing you can probably do with one of these is to use it as a dumb terminal --- USB ethernet devices work just fine with the OpenEmbedded distribution, so you may be able to telnet into (or out of) it. The phone's supported as an ordinary modem but I don't think I ever got it to work.
I'd suggest building the cable, trying to install the OpenEmbedded distribution above, and seeing what happens. It's not like you can make it less useful...