I'll try to provide some helpful perspective on this issue: please keep in mind that lawyers here cannot offer specific legal advice in this forum, because no attorney-client relationship exists. We can address only legal issues generally, and in hypothetical contexts. Also, please keep in mind that I am licensed to practice law in California only, and law and procedures differ from state to state.
The tort involved would be "Private Nuisance."
This would include damage to property value because of the activities of the neighbors, in addition to fear of safety in person or property; persistent unreasonable noise or crowding from parties, commercial activities, gunfire, etc.; increased traffic from unlicensed commercial business, in a neighborhood, etc.
But actions for private nuisance are difficult to sustain because every property owner has the right to the enjoyment of his property.
"Private nuisance" may be established where a neighbor's conduct is a legal cause of an invasion of another's interest in the private use and enjoyment of his property.
It requires the invasion be either:
1. intentional AND unreasonable (operating a criminal enterprise in a residential neighborhood is likely to be seen as "unreasonable," but then there would have to be proof of such by a preponderance of the evidence).
2. unintentional conduct but amounting to recklessness or negligent.
So, an individual suing another for private nuisance is going to have the burden to show how the conduct of his neighbors is harmful to the use and enjoyment of his own property.
Evidentiary records need to be compiled that tell the story of how the nuisance exists, and how it harms.
First, consider criminal complaints -- one against each residence you suspect may be in violation of criminal law.
Since you've spoken to a law enforcement agency, I presume you've considered this.
Individuals can swear out a complaint with the law enforcement agency -- Sheriff's Department or Police Department (many areas have both, but where there are both). Police should be able to suggest charges, but they will have to be violations that injure the individual, such as trespassing of the children, noise ordinance violations, zoning ordinance increased traffic or illegal parking, loitering, etc. [Keep in mind that if prosecutions proceed, the complaining individual may have to testify, and that may have repercussions.]
This would just be a first step: and remember it is entirely up to the law enforcement agency to investigate and then up to the district attorney whether to prosecute for any possible criminal violations. But even if they don't, the complaints will still be "on record."
Concurrently, if your municipality has specific zoning codes or building and property maintenance codes [e.g. no junk cars on cinder blocks in the front yard; no grass higher than X; housing in disrepair; buildups of garbage, etc], complaints about violations to the appropriate city agency (building inspection, code enforcement possibly health department) may also help.
Keep records on these complaints and get copies of any reports -- this will help establish a case later, and be help to any attorney you engage (and may reduce costs since you will have done some of the work!).
If you notice that police are called on or otherwise routinely visit those properties, or drive by, try to keep a log to show how often.
Another valuable contribution to evidence can be records that show a clear decline in area property values AFTER the problematic neighbors came to the neighborhood. Government records are best -- the property sales data from the Recorder's Office of neighborhood properties, but even commercial services such as Zillow.com can be used.
Keep in mind, legal action is expensive and time consuming. Direct engagement with the rental property owner may be more effective, faster, and less expensive -- after all, his property value is also declining!
I hope this provides some helpful perspective on private nuisance, and thanks for giving me the chance to respond.