To entirely use a (bash) shell to install e.g. Java 8u112 JRE do the following:
Download:
cd ~/Downloads
curl -v -j -k -L -H "Cookie: oraclelicense=accept-securebackup-cookie" http://download.oracle.com/otn-pub/java/jdk/8u112-b15/jre-8u112-macosx-x64.dmg > jre-8u112-macosx-x64.dmg
Mount:
hdiutil attach jre-8u112-macosx-x64.dmg
Install:
sudo installer -pkg /Volumes/Java\ 8\ Update\ 112/Java\ 8\ Update\ 112.app/Contents/Resources/JavaAppletPlugin.pkg -target /
Clean-up:
diskutil umount /Volumes/Java\ 8\ Update\ 112
rm jre-8u112-macosx-x64.dmg
To install the latest Oracle JDK (at the time of writing this answer it's Java 8u121 JDK) the various paths (besides the version number) are slightly different compared to the older JRE version. The URL contains an additional directory (i.e. /e9e7ea248e2c4826b92b3f075a80e441) and the dmg file contains a .pkg file instead of an installer app:
cd ~/Downloads
curl -v -j -k -L -H "Cookie: oraclelicense=accept-securebackup-cookie" http://download.oracle.com/otn-pub/java/jdk/8u121-b13/e9e7ea248e2c4826b92b3f075a80e441/jdk-8u121-macosx-x64.dmg > jdk-8u121-macosx-x64.dmg
hdiutil attach jdk-8u121-macosx-x64.dmg
sudo installer -pkg /Volumes/JDK\ 8\ Update\ 121/JDK\ 8\ Update\ 121.pkg -target /
diskutil umount /Volumes/JDK\ 8\ Update\ 121
rm jdk-8u121-macosx-x64.dmg