An object like Oumuamua originates in a solar system. This object has roughly the inertia of everything else there. I can imagine stuff on the edge of the accretion zone for a star that...WANDER off...
But come blazing into our system with enough energy to exit again? My only guess for something like that is stellar collisions.
What is a more informed answer?
The answer to 'how can it come blazing in with enough energy to exit again' is that if it started outside the solar system it would have been unusual for it to NOT leave again, since it would have accelerated towards the sun, then slowed down again by exactly the same amount on departure and left with the same velocity it started with, possibly in different direction.
The key here is gravity assists which can produce quite marked changes in the orbits of smaller bodies encountering gas giants, either causing collisions or boosting them away. This will tend to happen a lot in early system formation as gas giants clear their orbits. A more recent example is the way the Voyager and Pioneer vehicles did not intrinsically have enough thrust to escape the solar system but by getting assists from the gas giants 'stole' energy from the solar system to depart.
While departure velocity from the parent system will be low, the future encounters will tend to be with stars having markedly differing orbital velocities around the galactic core, so the process is unlikely to happen in reverse. This means the number of objects (and chance of one passing through our solar system) would tend to increase with time.
Determining actual source of 'Oumuamua is constrained by the available information, but a possible answer is a long period comet had an encounter with a Jupiter equivalent and was gravity assisted beyond the parent solar system escape velocity.
This is a very generic answer: A gravitationally bound system has a tendency to become more compact. As this happens, the gravitational potential energy becomes more negative. The energy that is lost ends up mainly as heat caused by collisions and friction. However, energy is also lost because of the tendency for small bodies to reach escape velocity and be cast out of the system.
A non-catastrophic gravitational interaction between two solid bodies tends to leave their kinetic energies more similar after the interaction than before (equipartion theorem). So the lower mass object usually ends up with higher velocity. Due to the natural distribution of velocities, many small objects can achieve escape velocity and will leave their original system.
Assume that 'Oumuamua was gently ejected from whatever environment it formed in. Then, how is it that it entered the solar system at 26.33 km/s?
This is actually expected. The velocity dispersion of stars in the solar neighborhood is 10's of kilometers per second. So, 'Oumuamua's velocity relative to the solar system is typical for the stuff that is flying around in our part of the galaxy. Even if its original velocity relative to its parent system was low, that system was probably moving pretty fast relative to the Sun, and therefore 'Oumuamua was, too.
Look at what has happened in our solar system:
56 objects that we know of have had gravitational slingshots that boosted them to higher than system escape velocity and they are now wanderers amongst the stars.
5 of these ejections were carefully engineered by NASA, but Jupiter has the power to eject on it's own and has been observed to do so once.
Orphan planets are more common than thought before:
Stars and even black holes likely harbor "rogue," or "nomad," planets that were kicked out of the star systems where they were born, new simulations suggest. At the same time, a separate study suggests nomad planets are much more common than thought.
Try creating your own "escaped planet":
https://academo.org/demos/orbit-simulator/
If you decrease the mass of the planet while approaching the sun (for example if the body is split in parts by gravity forces), the pieces will be launched away.
