#include <errno.h>
#include <locale.h>
#include <stdio.h>
#include <string.h>

int
main(void)
{
	locale_t locale;

	setlocale(LC_MESSAGES, "");
	locale = newlocale(LC_MESSAGES_MASK, "uk_UA.UTF-8", (locale_t)0);

	printf("%s\n", strerror_l(EINVAL, locale));
	printf("%s\n", strerror(EINVAL));
}

==========

strerror_l() uses created uk_UA based locale. strerror() uses jp_JP from
environment:

vbox# env LC_MESSAGES=ja_JP.UTF-8 ./strerror_l
Недозволений аргумент
無効な引数です
vbox#