Correct me if I'm wrong, but isn't an "interstellar" object, something that escapes the sphere of influence of a stellar object? If it's classified as an interstellar object, then once it escapes, it's not coming back (unless it's acted upon by at least one other stellar object).
By that logic, interstellar objects do not "orbit".
It's all about energy. If you drop a ball to a hard floor, due to friction caused by the elstatic reaction with the ground and, also, that of the air, it cannot bounce back to its orginal height. [Imagine if the ball actually bounced higher - Hollywood did and flubber was born! Nice flick.]
Comets don't suffer with energy losses due to friction. They simply gain KE as they lose PE on the trek inward, then the reverse happens on the way out. Just like a kid coasting down a hill on a bike will be able to coast up the hill if the climb is less than the fall (due again to friction).
When a comet comes from outside the Sun's gravity well, it will "bounce" back to a height from wence it came, though with an altered course. It can't have an elliptical orbit since these, by definition, require an object to always return, thus never escaping the Sun's gravity.
The KE it will have will be both the energy (velocity) it had when it came under the Sun's influence + the KE it gains from the fall. Therefore, it will always have enough KE to escape.
However, as usual, there are some side details worth mentioning. If something big (e.g. planets) gets in the path of any object, the object will either gain or lose energy for the reasons billslug
stated. If the object is traveling prograde it comes from behind the path of the planet, it will gain some extra velocity due to the speed of the planet in its orbit.
So the opposite is true, if our comet is traveling retrograde and passes by, say Venus, then the orbital velocity of Venus will have an impact on the comet causing it, and Venus for that matter, to slow down. [Note that Jupiter has many small objects in retrograde orbits around it for this reason.]
Of course, they have to be close to one another.
Space probes take full advantage of this both to speed up and to slow down, as needed. [Of course, I know you know this, but it may bring greater clarity for others.]
This is why the question of Leonard's hyperbolic orbit is so interesting. It, apparently, came from" sitting still" in the inner Oort Cloud, so how did it come with enough velocity to give it escape velocity. It had to get a push.