A couple of thoughts come to mind. One is that the seller of the real estate opposite the sign could accuse him of interference with their sale. I think that would require a civil lawsuit. The threat of getting sued might be enough to make him take down the signs.
My other thought is that there are few things Law Enforcement can do on private roads. However, there is a statute that might give them jurisdiction. Title 17 §2802. Miscellaneous nuisances says that, "...the obstructing or encumbering by fences, buildings or otherwise of highways, private ways, streets, alleys, commons, common landing places or burying grounds are nuisances..."
How does that get enforced? I'm not sure, but it may come under 17 MRS §2706. Penalty and abatement of nuisance. "Whoever erects, causes or continues a public or common nuisance, as herein described or at common law, where no other punishment is specially provided, shall be punished by a fine of not more than $100. The court with or without such fine may order such nuisance to be discontinued or abated, and issue a warrant therefor as provided. "
But then, there is ambiguity as to the meaning of the term "private way." In some places in Maine law, that revers to a "public easement," and therefore would not apply. But in other places in Maine law, the term is used to apply to a private road. 29A MRS section 101, subsection 58 says, "58. Private way. "Private way" means a way privately owned and maintained over which the owner may restrict use or passage and includes a discontinued way even if a public recreation easement has been reserved. " Going by that definition, it would apply.
You could ask your local law enforcement if these statutes would apply, and if there is anything they can do to enforce them.
Also, 23 MRS §3031 says, in part, "2. Private rights. A person acquiring title to land shown on a subdivision plan recorded in the registry of deeds acquires a private right-of-way over the ways laid out in the plan." So while it might be proper to post the road as being private, for the use of residents and their guests, or "not for public use," the wording on the sign in question would seem to prohibit use by anyone except the person who posted the sign.