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Increase productivity, use an autoformatter.

OP intentionally keeps trailing whitespace. Editing and review work increases because of it.

Not cleaned out trailing spaces, they are - debateable - intentional.

An autoformatter would fix that and also improve many other code attributes.

Questionable use of ERANGE.

The standard library never uses ERANGE to indicate a no conversion.

if( !isdigit( *p ) ) { // capture invalid strings like "-", " -xyz", 
        errno = ERANGE;

Additional u128toasc() improvements:

Rather than UB if size is too small, detect insufficient size and return an error code. (NULL, "", etc.)

Simplify with a do { ... } while loop to eliminate unneeded str[ --j ] = ( x + '0');.

Do not comment out relevant code

// #include "int128_test_5.h", with the // removed, fails the compile with error: unknown type name 'uint128'

OP failed to test the header file.

uint128 asctou128( char *s ) int128 asctoi128( char s ) char u128toasc( char s, int len, uint128 x ) char i128toasc( char *s, int len, int128 x )

Do not comment out relevant code

// #include "int128_test_5.h", with the // removed, fails the compile with error: unknown type name 'uint128'

OP failed to test the header file.

Header is missing code guards and int128 definition.

Use size_t for array sizing and indexing rather than int.

// char*               u128toasc( char *s, int len, uint128 x ) 
char*               u128toasc( char *s, size_t len, uint128 x ) 

Advanced: Consider leading with the size

The below allows for more error checking.

// char*               u128toasc( char *s, int len, uint128 x ) 
char*               u128toasc(size_t len, char *s, uint128 x     
 // or using later compilers
char*               u128toasc(size_t len, char s[len], uint128 x ) 

Minor: simplification

memmove( str, str + j, len - j );
return( str );

simpler as:

return memmove( str, str + j, len - j );

OP got lucky

What is the type and value of ( ~U128_MIN )?
~ is not operating on 128 bits.

#define U128_MIN 0
#define U128_MAX (uint128)( ~U128_MIN )