Gravity assists are pretty important for interplanetary travel. NASA uses them mainly because they can save time, energy, propellant, and expenses. But so far, all of the gravity slingshots have used the gravity of a large planet (such as Jupiter) to propel the probe farther into space.
Is it possible to use something smaller, such as a comet, to perform a gravity assist for spacecraft such as Orion?
Or is this possible, but only with smaller spacecraft/probes?
The Moon has been used as a gravitational assist in different ways.
See this answer, which links to this NASA page. The first video shows the two STEREO spacecraft use two and three passes by the Moon to leave Earth orbit and enter into an orbit around the sun.
Here is a GIF made from the frames of that .mov file:
You can read more about it in this answer, which also includes a discussion of the Nozomi spacecraft. I'm not sure if this counts towards your answer, since technically it is not interplanetary - the final orbit is around the Sun.
As long as the spacecraft is much less massive than the body used in the assist, it doesn't matter if the spacecraft is large or small. While the force depends on the mass of the spacecraft, the resulting acceleration is F/m. The simplest way to remember that to remember that a feather and a heavy weight fall to earth (or any body) at the same speed, in a vacuum. There are videos of a feather and hammer being dropped by an astronaut on the moon and of course in vacuum on Earth.
Earth-Moon system: The Moon's gravity is used in many different cases and scenarios to maintain or adjust orbits of spacecraft that will remain in the Earth-Moon system gravity, and are not therefore interplanetary. Some of those are also described in this answer, and you can read more about it in the pdf The Art and Science of Lunar Gravity Assist.
It is possible, but it likely won't do much. In order to perform a gravity slingshot, the object's trajectory has to be bent. It's a bit of a simplification, but imagine the escape velocity at the altitude you are passing over. The vector pulling the spacecraft down will be added to the incoming velocity of the object to bend the object's motion. If the velocity of the spacecraft is high, and the escape velocity low, then no practical gravity assist can be obtained. If there was a super dense small object, such as a black hole, passing very close to it could yield a usable gravity assist, but otherwise isn't possible. And there are issues with getting that close to a very dense object, namely that you have a window of only a few feet, as compared to 10s of miles for something like Jupiter.
