Ulysses tells us that his wife is old, and though we might reasonably expect Ulysses to be around the same age as his wife, the tone of the opening lines suggests that he at least feels younger than her. He tells us, after all, that he gains nothing from sitting around with an "aged wife"; maybe Ulysses and his wife make a bad match because of their figurative age difference.
You and I are old; Old age hath yet his honour and his toil (49-50).
Ulysses has no illusions about his old age, and he knows that the elderly are respected, but that they also have things to do (make wills, spend time with grandchildren, etc.). He tries to redefine the "toil" of old age, however, as something other than the mundane tasks of a grandfather; he wants "toil" to mean something like sailing to the ends of the earth.
The long day wanes; the slow moon climbs; the deep moans round with many voices (55-56)
Even though Ulysses is describing the onset of night, the description doubles as a reflection on old age; one could say that Ulysses is in the twilight of his life. He's not dead yet, and the day hasn't completely given way to night yet; that middle space between day and night seems to be of indeterminate duration. The present tense verbs ("wanes," "climbs," "moans") suggest actions that aren't fully completed yet in the same way that old age isn't death but isn't youth either.
And though we are not now that strength which in old days moved earth and heaven, that which we are, we are (65-67)
Ulysses describes a change in physical strength that we tend to associate with old age; the phrase "old days" makes us think he and his men were strong a long time ago. However, he never actually says he and his men are weak, only that they don't have the same strength they used to and that now they're something else: "one equal temper of heroic of heroic hearts" (68). Perhaps this sense of unity is a new kind of strength.