年寄り:としより； ('70s and up) this isn't rude per se, but if you want to dismiss or belittle what an old fart just said, this is the word you use.
老人；ろうじん；('70s and up) old person
年をとった：としとった：('70s and up) just like 老人 but it's an adjective.
年輩：ねんぱい； this is the most polite - you can even use it for someone in their '60s - but it's so formal you can't say '年輩の人’, you have to say ’年輩のカタ’