I could write a library in Common Lisp for all your app cares. It wouldn't mean you had to write your app in CLisp.
If you code in C++ or the lib uses C or C++ runtime library you will have a much bigger problem crunching in to 1Kb - the C++ compiler is more likely to use built-in stuff that you would need to emulate if you remove the libs, eg. new and delete.
As far as i know using OOP will be 4 bytes more for each function
I wouldn't say there's any hard and fast rule. Calling a function in a class means possibly one extra instruction, but it might get optimised away.
If you want to code commercially, you need OO skills. C++, C# and/or Java. (C# rocks, by the way). If you want to be a web designer and code Javascript, you might get away without.
Jim