“I've lived here for nearly 15 years, off and on.”

You moved to the U.S. after you graduated college, and you've mostly lived there since then. But you also spent a few years living in other places. Someone asks you how long you've been in the U.S., and this is your answer.

I've lived here for nearly 15 years, off and on.

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I've (done something)

When you're talking about an experience that started in the past and is still continuing now, you use "I've ___":

I've studied karate for over 12 years.

You can also use "I've ___" for something that just finished:

I've been driving for the last 8 hours. I can't drive any more.

nearly (length of time)

"Nearly" is similar to "almost". But people tend to use "nearly" when they're trying to make the number sound larger. "Almost" can make it sound like the number isn't enough, but "nearly" makes it sound like the number is high:

I spent nearly 6 weeks workng on it.

(do something) off and on

"Off and on" describes something that has continued to happen, but has not happened constantly. For example, if you dated someone, then broke up, then got back together, then broke up, and so on, you'd describe it:

We dated off and on for about 3 years.

It's not wrong to use "off and on" in written English, but a more formal way to express the same idea is "intermittently".