As their similar names suggest, the three Dwarves Ori, Dori and Nori were closely related to each other. All three were descended from a lesser line of the House of Durin, though their relationship is not canonically explained. From Tolkien's notes reproduced in The History of the Hobbit, however, it seems that Dori and Nori were brothers, and that Ori was their first cousin.
Ori was part of the company that followed Thorin to Erebor. Of those companions, Fíli and Kíli are known to have been the youngest by some fifty years and so, based on their known dates, it follows that Ori cannot have been born after approximately the year III 2809.