When I create a new Word document in Mac Mojave, multiple copies of Java install pop up. Every time.

Right-click on each one of those mounted installers on your Desktop, and select Eject "Java for macOS 2017…" When they are all unmounted, switch to your Downloads folder and move all of these Java for macOS installer files to the Trash, and then empty it. Reboot.

Now, either create a new Word document, or right-click on an existing Word document, and it should be the only thing that opens with MS Word.

What version of Word?

Look into the Free LibreOffice, it handles MS Office files like Word & Excel…

https://www.libreoffice.org/