No, they are not standardized, even within the same brand. Yes, you can go to box store and buy ALL new blades and arms (don't try and do just one) and depending on the age of the fan may extend it's useful life. And, since you're at the store anyway you might want to look at what they have for an upgrade!
Sorry, but having replaced many, many ceiling fans for clients, my advice is to buy a new one and go through the installation once rather than try and make an old, possibly dirty/abused/twisted arm/unblanced fan work at least on low speed without wobbling to death.