The MSDN documentation clearly states whether a C function or C++ functionality is Microsoft-specific or not. Different versions of the compiler support different parts of the c++11 and the upcoming c++14 standards.
You can easily use Visual Studio to work on a cross-platform project. You'd use CMake/premake4 for project generation, but unless you want platform-specific code, everything can be written in Visual Studio. It has better tooling than anything any other IDE I've tried can offer anything even close. Also, the Visual Studio's debugger is very, very good. For cross-platform projects, the most annoying thing for me is not related to the compiler, but that Windows implements Unicode via UTF-16 rather than UTF-8. The reason for that, like is the case most of the time with Microsoft products, is that they implemented Unicode support in NT when it was believed that 16 bits are enough to represent all people will ever need. Since Java was first implemented around that time, it is also one of the few tech stacks that do implement Unicode via UTF-16, as well.
The other two prominent C/C++ compilers - GCC and LLVM/Clang - also have non-standard extensions. Just look up POSIX, the libc is full of it. The fact that your Linux build compiles just fine with MinGW is only because the compiler is the same, not because it is more "pure" C or C++.
If you are one of the people that just doesn't like Microsoft, I would really recommend QtCreator and Eclipse CDT. Both work very well, and it is a matter of taste whether or not you like Eclipse. From what I understand, CodeLite uses clang for code completion, which means it must work very well and support C++11 (if using a recent version). In case you actually do work on Linux, you can try KDevelop as well.
Generally, if you don't use Visual Studio, I advice you to use an IDE that integrates with clang. XCode uses it, QtCreator may use clang (wip/clang), KDevelop (5) is switching to it, there is a plugin (llvm4eclipsecdt) for Eclipse that uses it, CodeLite can use it. Clang was built from the ground up to support IDEs - with code completion, syntax coloring and refactoring. What is best, this is part of the compiler, so it understands the code very well and automatically supports new language features.