unauthorized usage of power, Locating source of excessive energy use
Without any additional equipment (a clamp-on ammeter), it's not possible to determine how much electricity was used from one specific outlet / fixture. And, even then, it won't be able to determine how much was used in the past, only what's used once the equipment is installed.

Even so, it's not likely the neighbors used a significant amount of electricity from a single receptacle. Assuming you're in the US, it's 120V 15A, which is 1800W max - run that for an hour, and that's only 1.8 kWh (anywhere from ~20 to ~50 cents, depending on your rates). 5 hours a night for 30 nights a month, and it's "only" ~$30 difference in your electric bill - probably rather insignificant with AC running during the summer. And that's a worst-case scenario; if they are actually using it it's likely not anywhere near the 15A limit and so cost is much less.

If your electric bill is unusually / unseasonably high, check your HVAC first, followed by your water heater (if electric).