Non-elliptical orbits?

Hello fellow space cadets. I have a question.

Is it possible for a planet or other celestial body to have a non-elliptical orbit, for example, in a multi-star system?

In my head, I imagine a planet caught in an eternal lemniscate-shaped slingshot orbit around two stars. Is this possible?

What examples of highly irregular, non-circular/non-ovoid orbits have been discovered in our universe? Are there any?