“Is it against the law to refuse to give a police officer your age when he asks for it? Could it be counted as disorderly conduct?”
If you are not under arrest you do not have to tell an officer anything. If you are under arrest, our Miranda rights give you the right to remain silent. That said “disorderly conduct” is very subjective, and so it would be fairly easy for an officer to put you under arrest for disorderly conduct, and choosing arrest over revealing your age seems a bit silly. If you are doing something for which your age is an issue, and you are arrested, it will be a simple matter for them to find out your age anyways.