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.