I know that Japanese call their older siblings "older brother" and "older
sister."  But how do they say them?  Also, in Korean, the younger siblings

Elder brother = oniichan (oniisan, oniisama) or ani
Elder sister = oneechan (oneesan, oneesama) or ane

If you are speaking to your elder sister or brother, or speaking about 
them to the family, you call them by the honourific title 'onii*/onee*'. 
If you are talking about someone else's elder brother or sister, you also 
use this. If you are talking *about* your own elder brother or sister, 
*outside* the family, you call them 'ani/ane'.

There are also younger sibling titles, too

Younger brother = otoutosan or otouto
Younger sister = imoutosan or imouto

When you are talking to your younger brother or sister, you call them
by their name. If you are talking about someone else's younger brother
or sister, you call them 'otoutosan/imoutosan'. If you are talking about
your own younger brother or sister within the family, but not to them,
you call them 'otouto/imouto'.

call their older siblings a different term when it comes to gender. 
Example, a male may call his older sister "nuna" in Korean.  BUT a female
will call her older sister "onni."  Do they do the same thing in Japan?  If

No, but I guess the 'san/chan/sama' ending may differ according to who
is talking. Like Kodachi calls Kunou 'oniisama', and Akane calls her
sisters 'Nabiki oneechan' or 'Kasumi oneechan'.

they do, please tell me what they are called, if not, just tell me the
terms that they use to call their older sister/brother.  Thanks.

Lots and lots of rules, all to do with who you're talking to at the time.

Kun-chan...