I'm assuming that the machine sewed just fine before it was oiled. The tensions were set to work w/minimal oil. There was more resistance. Now that it has been oiled, there is a good possibility that you will need to reset your tensions because there is less resistance. Since it's breaking at the bobbin, that is where I would start. It probably needs to be loosened. Mark on the bobbin where you start before you loosen the screw. And turn it very slightly, then check to see if it stops breaking.
Did it sew well w/that thread before the oiling? If it did, then continue to use it. If this is a different thread, then change to one that you haven't had a problem with in the past.
Good luck, we all know how frustrating that is.