Can police officers enter a party on a private property if there are underage teens?

Probable cause means that the officer has a reasonable suspicion that a crime is being or has been committed. That reasonable suspicion can be based upon complaints from neighbors or others who would have a good reason to know about what was going on at the house or on things the officer can personally observe when at the location. Providing alcohol to minors is a crime that would allow an officer to enter a private residence. The court-imposed consequences to the owner of the property, the person(s) in residence, and the person who provided or made the alcohol available can range from a fine to jail time. Social consequences can include loss of employment, social shunning, loss of opportunities at school/work/clubs/events, increase in insurance rates, and other limitations.

It doesn't matter if the property is public or private when it come to a police officer entering property. What matters is that a legal threshold has been met. If the police have a warrant, probable cause, or exigent circumstances they can enter your property. Police don't just look the other way because a situation arises on private property and teenagers are involved.