Locale-independent

OK, it's a bit tricky indeed: all the locale-dependent functions you mentioned aren't standard. They are Microsoft proprietary extensions to the Standard Library. Recentky Microsoft submitted a proposal to include these functions in ANSI C and C++ but that doesn't mean they are already standardized. So it all boils down to which OS and compiler you're using. If your standard headers (math.h, stdlib.h etc.) don't have these functions, then don't sweat it -- it's not just a matter of getting the header file bt also the binary lib files.
C++ defines the <locale> library for locale-sensitive apps and wchar_t functions and classes. C has its own <locale.h> header.

To ensure localizability, stick to wchar_t and the standard wchar_t functions. Almost every ANSI function that takes char * has a wchar_t equivalent: wstrstr, wstrcpy etc. These functions *are* standard so you can expect them to be supported on most platforms. What's not in the Standard yet is the _l functions so you should avoid them.
Other than that, localization is a vast topic. To do it right, you need to plan in advance what yoru app is supposed to do and how much localization you want to offer: is it just the error messages being displayed in different languages? Or do you also intend to use different temperatures (Fahrenheit vs. Celsius), different decimal points (. or , ), date formats etc. The standard C++ <locale> library supports all of these but using it isn't exactly a trivial task.