I want to copy the data folders from a previous ubuntu(14.04) partition

I also have a small swap partition - I would like to preserve the data on that too if possible.

There is nothing useful on the swap partition and you don't need to back up that one.

nothing I do allows me to copy to an external hard drive

This is expected, because the home directory belongs to the user with id 1000 (called simon):

drwxr-xr-x 39 1000 1000 4096 Aug  3 14:21 simon

For some reason you have 3 home directories but the concept is the same for the other two.

This user does not exist on the live DVD, which you are running as user ubuntu. For this reason, the permissions prevent you from loading the contents of the home directory.

You must run the file manager as root. I have discussed this operation on SuperUser, so let me just quote my other answer (slightly adapted to your case):

Run:

sudo nautilus /media/ubuntu/ebe2a6ba-9cb5-4279-8352-5082b8dd4d5e/home

On many Linux distributions, you can try to open a directory with the default file manager using xdg-open even if you don't know its name:

sudo xdg-open /media/ubuntu/ebe2a6ba-9cb5-4279-8352-5082b8dd4d5e/home

Beware: you now have full permissions on the files on any connected drive. Pay attention on what changes you perform.