When people ask you your age, should you be considered a nominal age or a year old? Why do people joke when I say one year old?

It doesn't really matter. Every place has different habits. In some places, age means nominal age, while in many places, it means complete age.

I suggest you see the other person's intention of asking age before you decide. If the actual age is counted by unit, you must fill in one year old, and you need to fill in the year, month and day. But if friends or strangers ask at random at the beginning of acquaintance, they can report a one-year nominal age. There's nothing funny about it.