elder、older这两个词均是old的比较级,在用法上有所区别。elder本身也是形容词。 
1.elder表示“前辈的”、“年纪较长的”,仅用于同一家庭成员的比较;older则不限于此。
My younger son is five and my elder son is nine。我的小儿子5岁,大儿子9岁。 
Tom is two years older than I.汤姆比我年长两岁。 
2.elder在句中只用作定语,不作表语;older两者皆可。
My elder sister does her homework all by herself. 我的独自做作业。 
His elder son got married last week. 他的长子是上星期结婚的。 
I think his mother is older. 我认为他的母亲年龄大引起。 
3.elder只能用来指人;older既可修饰人,也可修饰物。例如: 
限于My elder brother joined the army when he was only fifteen.我哥哥年仅15岁就参了军。 
This dog is older than any other dogs here.这条狗在这里是最老的一条。 
I have a sister older than myself.我有位比我大的。 
It is said Mr Chen is over ten years older than Mrs Li.据说陈先生比李女士大10多岁。
4.elderly是形容词,“较老的”。elderly是委婉用语意为上了年纪的,一般不说old man而用elderly man代替,the elderly泛指老人。
His  mother's  elder  sister is an  elderly  woman now.