* Older brother: お兄さん (onīsan) - This is a polite form. 兄 (ani) is the more informal, direct form.
* Older sister: お姉さん (onēsan) - This is a polite form. 姉 (ane) is the more informal, direct form.
The polite forms (-san attached) are generally used when speaking to or about the older sibling, or to someone else about their older sibling. The informal forms are typically used when speaking directly to your older sibling (though even then, Onīsan/Onēsan might be used out of respect depending on the family dynamic and age difference).