There are a lot of ways to communicate something about your age, and a lot of them depend on the social aspects and pragmatics (the implications of what you say).
Grammatically, in English, they all use 'to be' rather than the usual Romance 'to have'.
From your title question, it seems the social situation is that you are not saying exactly the number of years since your birth. But for reference that would be:
I am 27 years old.
But to say it without the exact age, you'd say something like:
I'm almost thirty.
I'm about thirty.
I'm in my twenties.
I'm in my late twenties.
I'm having a hard time imagining someone naturally saying "I am not yet 30", unless the query were something specific like "We're looking for someone 30 or older? How about you?" and a similar situation would apply to "I am younger than thirty.". You word for word translation "I am less than 30" is, while grammatically correct, and semantically correct, just not how you say it in English, and sounds a bit robotic, and overly mathematical.