They certainly look exactly like edible ones. Why not taste one of the darker ones? If its horrible you can spit it out without swallowing (poisonous fungi are identified using this test so its safe enough). If they taste good eat them. I would be totally astonished if they weren't good as have never come across anything else that looks like this.
If they belong to next door's tree the legal position is you may remove them and the branches they are on but you should give them back to the owner...

Certainly looks alright. The only thing I'd add to Steragram's advice is to chew one and spit it out. Then wait for a while as some berries contain chemicals that can take a while to manifest their unpleasantness generally by making the mouth feel numb.

Do they hang from a single or double stem?