I do notice accents immediately, and find them interesting. I enjoy listening to people with accents other than mine. It's funny, because when we moved from Minnesota to Texas many years ago we had a hard time understanding people here....and some of them had a hard time understanding us. Not only due to heavy accents, but also due to some different terminology -- such as Minnesota's "stocking caps" are Texan's "tobagans". Minnesota's "kitty corner" is Texan's "katty corner." Minnesota's "pop" is Texan's "coke". (All soda pops are Coke's to many Texan's. My neighbor would ask me if I wanted a coke, then ask what kind. We one time went to a grocery store looking for the pop, and they didn't know what we were talking about until we said coke.)
We loved listening to Texans talk. Now, we don't notice Texas accents......unless they are the real heavy, deep Texas drawls. But.............we do notice the Minnesota accents! Funny how that changes after time. We no longer have the sharp Minnesota accent, but we have enough of it left that Texans can detect it. When we go back to Minnesota on visits people hear our Texas accent.
I can't really pin point the origins of different accents except those that I am very familiar with............like Minnesota and Texas. But I can usually determine the general US region an accent is from. Some foreign accents.....such as Mexico, France, Italy, England, Australia, Africa.....are somewhat familiar to me, and I can usually make a good guess as to where they originate, but I'm rather limited on that.
I'm not sure what you mean by class or age............if you mean in relation to accents, or if we notice different classes or ages. If it's in relation to accents, I guess I somewhat detect a difference in some people as to what social class they may be in, but not often. And age...........no, I don't notice a difference there as far as accent.
If you mean do we notice different classes or ages, I do notice somewhat, but not really. It's not something I look for or that really stands out to me unless it is very evident. Actually, I do notice the elderly because I enjoy them and really have a heart for them, but other than the very young, or the very old I don't differentiate or group people.
I was born and raised in Minnesota, moved to Texas when I was 30, and we have been here in Texas for 23 years. I consider myself to have an accent that doesn't really belong anywhere because it is now Minnesota Texan.
Interesting subject. :)