function compare_strings(a, b) {	
	a = a.toLowerCase();
	a = a.replace("ä", "ae");
	a = a.replace("ö", "oe");
	a = a.replace("ü", "ue");
	a = a.replace("ß", "ss");

	b = b.toLowerCase();
	b = b.replace("ä", "ae");
	b = b.replace("ö", "oe");
	b = b.replace("ü", "ue");
	b = b.replace("ß", "ss");

	return (a == b)? 0: (a > b)? 1: -1;
}

sort strings (that contain umlauts)

sort, array

JavaScript