Talk to your DBA.
Probably the most straightforward way is to set up an Oracle database link between the two database schemas, plus appropriate GRANTs and synonyms on the relevant tables. Then you can just use SQL to move the data from either end whenever you want. Watch out for integrity constraints e.g. you need to make sure the parent records exist before you insert the children to the target database, and any primary keys must be unique of course. You can switch constraints off while you're loading data then re-enable them afterwards, but that's risky if other applications are writing to the same tables, and it's probably not worth doing for these small volumes of data. You will need to keep an eye on the sizing for your target system, however, as it sounds it will be accumulating data fairly rapidly. Maybe look at partitioning the tables, e.g. by date, which can also help to speed up the transfer and improve management of the data. Again, you need to talk to an experienced Oracle DBA for proper advice on this stuff.
Another option would be to use the
PL/SQL API for Oracle's DataPump bulk data-loader which allows you to export data programmatically to flat files (in an Oracle-specific format) and import them into another database. Your DBA will need to advise on this e.g. you'll need access to appropriate directories on the DB server etc. DataPump is very fast, but probably a bit too complicated for your needs.
But plain old SQL is probably easier for what you want to do, and for the small volumes of data SQL you're moving every day SQL should be plenty fast enough.
Either of the above options could be coded as PL/SQL packaged procedures that could then be scheduled easily e.g. to run overnight. You can even use the Oracle scheduler in the database to do this so you don't need any Java at all here.