When you bought your property you had to obtain a Title Search from a Title company. That search would have listed all the boundaries, and easements on your property. The easements would have included all utility easements, easements to other properties, etc., in fact any legal access to anything or for any purpose across your property. Then the Title company would have issued a Title Insurance Policy.
Pull the title search document from your purchase documents and read it for any easements that would cross any part of your property other than the utility easement road that accesses other properties. You know about that one, but if there is no public easement to that utility easement from the other neighborhood, then you can block access.
Remember that even though there is an easement across your property not everyone is entitled to use it. Utility easements are for that purpose only and are granted to utility companies to maintain the utilities. The utility easement does not allow any member of the public to use it, only the utility company named.
Easements along that road that are for access to other properties are only for access to those properties by the property owners, and their visitors (personal or business.) That does not mean that any member of the public can just walk along that road. You can also post that road as "No Trespassing - Private Property" and also put up a sign reading "Private Road - No Egress" or "Private Road - Dead End". We are on a dead end private road and any neighbor has the right to stop anyone we don't recognize and ask where they are going. Since we all know everyone on the road, we recognize the names. We all feel safer this way and over the years it has cut down on strangers driving through to sight see or case properties.
Definitely post "No Trespassing - Private Property" signs along the utility easement and along your property where people are crossing to that road across your property. Once you post the signs you have legally notified the entire world that they are crossing private property. This will prevent the establishment of an "Easement by Prescription" or "Easement by Adverse Possession". If there is no easement across your property to the private access road, then fence it off.