Using GNU sort 5.93 on OS X, i get the same ordering in the default locale (which is probably one of en_GB.utf8 or en_US.utf8 - something which doesn't know Korean, anyway). However if i set LC_ALL to ko_KR.utf8, i get the three-character strings sorted first. The sets of two- and three- character strings keep the same order between themselves.
Note that all the three-character names begin with '강'. What this looks like is that '강' sorts after all the other initial characters in a naive locale, but sorts before it in Korean. If i insert a nonsense string made of one of the three-character strings with the initial character replaced with the initial character of one of the two-character strings (that is, "양호석"), then that sorts in with the two-character strings. This shows that the sort order is nothing to do with the length of the strings, and simply to do with the sorting of '강'.
I have absolutely no idea why '강' sorts after the other characters in my locale. '강' is at code point U+AC15. '곽' is at code point U+ACFD. '차' is at code point U+CC28. If the sort was on raw code point, '강' would sort before the other characters, as it does with the Korean sort.
If i sort these strings with Java, they come out with the '강' strings first, like the Korean sort. Java is pretty careful about unicode matters. The fact that it and the Korean sort agree leads me to think that that is the correct order.
If you encode the characters in UTF-8, then its first byte is 0xea, which again would sort before the other characters, which encode to bytes starting with values from 0xea to 0xec. This is presumably why collate "C" gives you the right result - that setting causes the strings to be sorted as strings of opaque bytes, not encoded characters.
I am completely baffled as to why collate "ko_KR" gives the wrong result.
LC_COLLATE=ko_KR.utf8 sortwith your sample data fed into stdin. If the result differs from postgres, it's a postgres problem, otherwise it's a libc problem (btw, what OS is this?)