As far as I can tell (and have experienced),
oracle-java8-installer will update your Java version for you.
Whenever a new version comes out, the installer is updated with the new information. The next time you run
sudo apt update, this new installer version will be reflected. Running
sudo apt upgrade will install the new installer, which will then (in turn) install the new version of Java.
Note that this will only work if you've installed Java through the package. If you used the raw tarball, this will not work nearly as well (or at all).
It is important to note, however, that this will not increase your "major" version (so Java 8 will never upgrade to Java 9, unless you install Java 9's installer).
This method of Java installation offers no notification, so you just need to run the
apt updater. Depending on your system configuration, Ubuntu may offer a general update notification. See the Software and Updates app for this setting.
Generally speaking, very few packages installed through Apt will have their own update notification system (though some, especially launcher-only packages usually will). Instead,
apt will take care of things and bundle it with all the other updates. To some, this centralized package system is one of the biggest benefits of Linux over other operating systems.