How to get apt to make files in /var/cache/apt/archives always world-readable?

APT is affected by the umask of root which is inherited from the global setting from /etc/profile. You've likely a line in it with umask 077. To make the files world-readable by default, you'll have to change it to:

umask 022

To change default the permissions of existing files, run:

sudo chmod 644 /var/cache/apt/archives/*

To copy archives from one machine to another, you can use netcat. On the source machine (ip = 10.0.0.2) which has .deb files to be distributed you need to install netcat-traditional and run:

cd /var/cache/apt/archives
tar c * | nc.traditional -l -p 1234

Replace * by the files you want to copy.

On the target machine, run:

nc 10.0.0.2 1234 | sudo tar xv -C /var/cache/apt/archives