"I'm not even old."
The literal translation is "I am not nor would I be old", but the intended meaning is that the speaker is not old, and it is emphasizing this point.
Here's a breakdown:
* "no soy" = "I am not"
* "ni" = "nor"
* "sería" = "would be"
* "vieja" = "old"
The phrase is often used to express that someone is younger than they look or to refute someone's assumption about their age.