How does C code call assembly code (e.g. optimized strlen)?

The C standard dictates what each library function must do rather than how it is implemented.

Almost all known implementations of C are compiled into machine language. It is up to the implementers of the C compiler/library how they choose to implement functions like strlen. They could choose to implement it in C and compile it to an object, or they could choose to write it in assembly and assemble it to an object. Or they could implement it some other way. It doesn't matter so long as you get the right effect and result when you call strlen.

Now, as it happens, many C toolsets do allow you to write inline assembly, but that is absolutely not part of the standard. Any such facilties have to be included as extensions to the C standard.

At the end of the road compiled programs and programs in assembly are all machine language, so they can call each other. The way this is done is by having the assembly code use the same calling conventions (way to prepare for a call, prepare parameters and such) as the program written in C. An overview of popular calling conventions for x86 processors can be found here.

When C code is compiled by gcc, it's first compiled to assembler instructions, which are then again compiled to a binary, machine-executable file. You can see the generated assembler instructions by specifying -S, as in gcc file.c -S.

Assembler code just passes the first stage of C-to-assembler compilation and is then indistinguishable from code compiled from C.