She sounds mentally ill----(& unfortunately reminds me of the only grandmother I knew...luckily for others, my grandfather had provided for her before his death, and she had enough structure and space around her to prevent her toxic illness from affecting people outside the family...and lucky for me, my mother did not allow her in our house after her one, very nasty, visit...though we did see her each summer when my father was on vacation - his mom- and that was enough to cause nightmares) .
I would report each disturbance, and if the neighbors do likewise, she may end up in some sort of care setting--- Talking to her clearly will not help---I would avoid arguing with her, it will probably fuel her anger/spite/paranoia, or trying to make adjustments to please her, just quietly take information down and call the PD or SS whichever seems appropriate in the situation, she will not respond to logic, or pleas, or anything but what is inside her head----she may let down her guard when a nice young policeman sits with her, but what she tells him will still be just what is in her (likely paranoid) mind...she might even make him promises she cannot keep, or have delusions of being the victim...
So sorry for you and the neighbors.