There's not a lot of reason to pick up Objective C unless you plan on targeting Apple.
C++ is also important when targeting Apple. Objective-C is the language of the Cocoa API (Mac OS X and iOS), however there is no need to use it beyond code that makes Cocoa based system calls. And getting C++ and Objective-C code to call each other is trivial.
Personally I recommend separating UI and platform (OS) specific code from an app's core functionality and implementing the UI/platform-specific code in whatever the native language for the platform is and implementing the core code in C/C++. This leaves the core code portable, ready to target other platforms. I have iOS apps where the core code can be compiled in a console Linux environment and exercised by various scripts (regression testing) and in a random manner (fuzzing).