I also tried:

use Inline C => 'DATA',
                LIBS = > '-lalib -lanotherlib',
                INC = > '-Iinc';
[download]

This makes it possible to build the module (because it can see the definitions) but when it runs it spits out a relocation error because the functions in the included library aren't actually compiled. Also tried combining the two:

use Inline C => 'DATA',
                LIBS = > '-lalib -lanotherlib',
                MYEXTLIB = > 'inc/somecode.o',
                INC = > '-Iinc';
[download]

This won't build of course since somecode.o doesn't exist. Perhaps there is a way to modify Makefile.PL to do a:

gcc -o inc/somecode.o -c somecode.c

before building the module itself? Where gcc is set to whatever CC is in the Makefile of course.