Erebor was lost for 171 years, meaning that if we go for movie canon (which I will for this story), Ori will have been born less than 100 years after Smaug came. Book canon makes Thorin 24ish (preteen for a Dwarf) around Smaug, so I'll make Dwalin around 190 now. (four years younger than Throin, because I can.) Ori is 76 years old in my head canon, making him just past maturity and one year younger than Kili. Dori is around Thorin's age, and Nori was born a year or so after the loss of Erebor, so to not make him too much older than Ori. (I can imagine that Nori was just reached maturity when Ori is born, being as having children is a hard thing for dwarven women, so a long age-break is normal.)
Out of the three Ri brothers, Dori was the only one to have found his One, at this point. They had met at Erebor, when Dori was still a young dwarfling. Nori hadn't been born yet, still nothing but a twinkle in his mother's eye, but sometimes, when the eldest was in a pleasant enough mood, Dori would speak to Ori of his One, and Nori would listen at the door.
When Dori spoke of his One, he spoke of a young dwarfish girl with flaming hair and a smile that reminded him of the finest gems. He spoke of a feisty personality, so unlike Dori's own, that challenged him and made him better. Dori spoke a lot of things about his One, but in the end, neither Ori nor Nori knew who she was, nor where she was now.
At times, Nori suspected that neither did Dori.
This, however, might not be true. Judging from his brother's lack of searching, Nori had little hope left in him, that she was alive out there somewhere. Nor that there was really any doubt that she was. Because if there was doubt, Nori couldn't imagine that his brother would be anywhere but out there, searching the world for her.
He knew that the youngest of them wished with all of his heart that she was out there, searching for Dori. He held stubbornly onto a childish hope that the flame-haired girl from his brother's tale, was currently spending everyday looking into crowds, hoping to see her One looking back at her. Ori was a romantic in that sense, never believing that his brother could have lost his soulmate.
Nori knew this because he had witnessed Ori talking of his and his brothers' Ones more than once with their mother, before she passed.
Nori spend more of his time listening at doors, than he cared to admit.
Back then, their mother had told her youngest child every romantic story she had ever heard, encouraged the then dwarfling to believe in them, in a vain hope that it would spare him from the harsh reality. A hope that both Dori and Nori had kept alive after their mother's death.
Not all dwarves recognize their One straight away. It was often seen, especially with the younger dwarves, that it took years before the feeling on rightness settle into a dwarf's bones, until their finally looked into their intended's eyes and saw nothing but beauty and happiness reflected back. This could mean that Nori had, perhaps, already met his One. His One could be in the Blue Mountains, going about their everyday life, blissfully unaware that Nori was there as well.
Of course, it was also entirely possible that Nori had never and would never meet his One, but he tried his best not dwell one either of those