Do Oracle databases use Java internally? My question is fairly simple. Is Java used internally by Oracle in their DBMSs?
No. 

All (standard) packages are written in PL/SQL. 
The DBMS engine itself is written in C

Edit:
Oracle does include a JVM which runs on the same machine as the database itself, but that is not used to run any "DBMS related" code. 

It's only there to run stored procedures/functions written in Java.