Now if you want to speculate even further into the future, cumulative effects of the merger will eventually destroy the solar system due to gravitic disruption of the neighboring stars..
Gravitational effects of nearby stars are unlikely to be felt at all. The gravitational effects of the galaxy as a whole will be tremendous, but they would barely differ from one side of the solar system to the other. The solar system won't notice any of them as a result. Aside from ejecting the entire system, or grabbing it, Andromeda will hardly affect a single orbit in it.
Eventually it will but on a much larger timescale than I was originally talking about...but still in a finite timescale before the end of the universe. Its a cumulative effect.
We should definitely see solar system effects through radiation and such in the merged galaxy, as I said our solar system won't be part of it. Humanity as a galactic entity will likely be though.