Today I've written Java, Python, C++, and SQL (if it counts). And I've been at work for less than 2 hours.
If you do this regularly, then the mental shift becomes negligible. It has nothing to do with multitasking. It's just like walking for a while, then driving a car, then driving a bike, then swimming. No problem, because they're sequential things.
Regardless, the point is to complete one task before moving to the next. I tend to define tasks in terms of a concrete functionality, fix, or such. Often that task is accomplished with only one language, but it may require several of them. For example, when working with JNI, you'll typically make changes to both the Java and native sides in parallel.
Do you code in stages based on progress on each task switching seamlessly between languages/IDE/Environment
It's important to be able to switch seamlessly between IDEs, editors, environments. Usually I keep them all open all the time.
Do you apply the same coding style /conventions on all the languages(Not syntax)?
If it's an interface over which two languages are talking, then yes - variable names and such must be similar. Otherwise, I try to apply the typical coding style of that language.