Here are the distinctions in use for elder/eldest and older/oldest::
1) "elder/eldest" can be used ONLY of people, but "older/eldest" can be used for anything (people, animals, things)
2) "elder/eldest" may be used to emphasize rank or seniority ("oldest" does not do this), and need not be emphasizing age [related to this is the use of "elder" as a noun for someone with a position as an "elder" (a ruling position) in a church, town, etc]
3) "eldest" is used in comparing a group ("my eldest son"/"the eldest of my three sons"), but "oldest" can be used in a more absolute sense ("the oldest man alive")
So, in the case you mention you could technically use EITHER "elder" or "older" could be used, but "elder" would likely suggest rank/superiority, so if ALL you want to do is speak of AGE, use "older".
http://www.thefreedictionary.com/eldest
http://www.thefreedictionary.com/elder
For what it's worth.. on why we even have TWO forms: the words elder/older and eldest/oldest are from the same root word, but "eld-" follows a pattern common in Germanic languages, where when a suffix with an i-type vowel is added, the vowel in the preceding syllable changes to an e or i to become more like it. (The same sort of change, called "i-umlaut" is easy to see in German "alt" > "aelter/aeltest"; it also explains a whole set of irregular plurals in English, such as geese, mice, men and the archaic 'brehthren'.)
http://www.wmich.edu/medieval/research/rawl/IOE/pronunciation.html#pronounce:imutation
http://en.wikipedia.org/wiki/Germanic_umlaut
Thus "older/oldest" is, originally, simply a more modernized (younger!) form of "elder/eldest". But as often happens when two forms mean the same thing, one or both of them start to take on specialized uses.