Thanks to all for the replies, the links to legal sites etc. helped immensely.
"I wouldn't say anything to the landlord, because it is eventually going to be over. As uncomfortable as you are right now, think about those poor children having horrible parents and no home."
To me, that statement sort of implies that "at least I'm not as bad off as the kids are," and that seems illogical. Their situation is not helped any by my being miserable in my own home (where I pay over $900/ month rent and am an excellent tenant). Keeping quiet and putting up with all of this nonsense because I feel sorry for the kids does not make sense to me, nor does it help anyone, and thus that doesn't provide a basis for keeping quiet about this.
But, regarding everyone who has said these kids need to be in the system and that there's something going on over there, I agree. The kids range in age from 15 to 9 and they are often home alone. After they blasted rap music at 8 am Saturday morning and woke me up (from the other side of the house), I called the landlord and left him a voicemail informing him that I'm going to report the neighbors for leaving the children home alone, but that I want to touch base with him first. Perhaps there is already something in progress, I have no idea; but I feel as though I need to at least speak to him before I do anything else.
In the meantime, the childrens' welfare aside, if they won't be moving out anytime soon I may look into breaking my own lease. My state has an implied "quiet enjoyment of property" clause in every lease, and according to a renter's rights group I talked to on the phone the other day I may be able to get out legally. Wish me luck on this.