What causes oil and diesel to mix and causing a lot of smoke on an Isuzu 4jx1 engine?

If you mean that diesel is somehow getting into the oil sump and the oil level is rising then this is quite common with this engine and is due to either the injectors or the injector seals failing. Loads is on google about this problem.

This car was recalled by Isuzu to have it fixed. If a car wasnt recalled then its a time bomb and if injectors need replacing it costs a fortune.