'something' is a number in this case, if you say 30 something, it can be 31, 32, 35, 37, etc. 

It's an expression that can be used to describe a range of ages. For example, somebody could say "This is not a job fit for a twenty something person fresh out of school": the speaker expresses that it doesn't really matter if someone is 20 or 24, for them all people that age are unfit.

People don't say often "I am a 20 something..." to tell their age, unless it's to express a general idea about themselves, like the belonging to a category of people, a category that the listener should know the charateristics of, like "Are you suprised I can't find a job? I'm a 40 something with outdated skills, in this economy".

got it, thanks Mike.

You wouldn't say "my age is turning ____", but rather "I'm turning ___". 

As as has been pointed out, you would only use that sentence structure when you're specifically trying to talk about people in a wide age group. Therefore you would never, unless joking, say that you're turning thirty something. You would just say how old you're going to be. You could, however, say that about someone else if you didn't kbow their exact age. 

thanks Dina and Berze :-)