Since the Arduino libraries are built on top of avr-libc, they too are available for your use. Note that they aren't as "user-friendly" as the Arduino libraries (the Arduino libs consist of many wrappers which abstract a lot of work away, among other things), but many of the library functions (such as strlen) are simple enough to grasp, especially with an example or two.
As far as I know that function and a lot more are part of a tipical C compiler, so just get a good book about C programming.
More accurately, they are part of the standard C library set. However, the AVR version may have various differences from what you would find in the "full" version due to it being optimized for the AVR microcontroller family, so it would be better to reference the link I gave instead.
If you aren't well familiar with C/C++, though, I would recommend a book or two. One of the better ones is "C++ How to Program" by Deitel/Deitel. Its widely used in introductory (and likely advanced) C/C++ courses in universities and colleges.