Why won't the Milky Way colliding with Andromeda affect the Solar System? According to Wikipedia


  Such an event would have no adverse effect on the system and the chances of any sort of disturbance to the Sun or planets themselves may be remote.


I'm imagining that this is because the distance between stars is so big, it'd be highly unlikely for any star to actually collide.

But the Oort Cloud is 2 light years in diameter. Given that the average distance between stars in the Milky Way is about 5 light years, that's almost half way. If Alpha Centauri had an Oort Cloud of the same size, we'd already almost be overlapping each other.

Assuming that we're not the only star with an Oort Cloud, isn't there a high probability that the Sun will actually be inside the Oort Cloud of a passing star?

I would imagine this would because the Sun and our planet would be bombarded with lots of comets which have been thrown off their orbits by either the gravity of the Sun or the passing star.
Outside my field, but collecting information from the Wiki article, I can make an attempt nevertheless:

You're right that we will probably pass through Oort-like clouds of other stars. But the largest of the planetesimals of the Oort Cloud is measured in kilometres, whereas the distance between these objects is measured in AU, so the total cross section of object compared to that of the cloud is still miniscule. Smaller objects are larger in number, but still it's a very low probability.

Gravitationally, the clouds also won't affect us. The total mass of the Oort Clouds is probably of the order of 10 Earth masses, i.e. much smaller than the Sun.

The outer parts of the Oort Cloud is only loosely bound to the Sun. I suppose the best evidence that we won't have any major collisions is that then we would already have similar objects bombarding us from our neighboring stars' clouds.