This page explains how to install OSX (tiger) on an eeePC.
Note that I have no mac expertise.

A good installation script can be found at http://eeepc-osx.wikispaces.com/Tiger_install
In the first step 12 (at customize) the thing to check is "JAS Intel 10.4.8 ATA kexts incl". This is the kernel patch that is referred to.

The time needed to install OSX will depend on the speed of your DVD-rom. Expect something between 30 and 60 minutes for step 3 to the reboot in step 12.

After installation 2.7 GB of your SSD card will be used, leaving 1GB for other things (assuming you have a 4G eeePC).

Therefore installation on a 2G system is not possible.
Whether it is possible to install on an external device (e.g. a USB flash disk, a USB hard disk or an SD or SDHC card is unknown by me).

I found the performance not too good and although it looks good, there is not much in it for me, so after 30 minutes of playing around it was already removed from my system (but I can vouch now that it works :-) )