scp and rsync to transfer data from Linux to Android
Many things are possible. Installing an SSH Server app (e.g. SSHelper or DigiSSHD / SSH Server) would give you the possibility to login via ssh, or remote-copy via scp.

Terminal IDE (available only for Android 4.4 and earlier, according to the app description) gives you a quite complete package, even including the famous Midnight Commander, and a lot more useful tools:


  javac, java, dx, proguard, aapt, apkbuilder, signer, ssh, sshd, telnetd, bash 4.2, busybox 1.19.2, vim 7.3, nano 2.2.6, midnight commander 4.8, htop 1.0, TMUX 1.5, rsync 3.0.8, git 1.7.8, BitchX 1.1 and a nice terminal emulator are all available.


(emphasis are introduced by me to pick the items your question was for)

So except for Unison, the latter package should cover your needs :)