I've had similar problems with inherited C++ and Java code. It can be very hard to track down leaks and performance problems when they aren't really true leaks!

You don't need to find the entry point. With bad OOP, that can be very tough. I'd recommend you make a utility class and in each constructor log the constructed object with the utility class, or (simpler) just print out to STDERR when you construct things so you can analyze the output later. Debugging by STDERR is gross sometimes, but it's incredibly versatile when trying to understand what your app does.

I like to have a Util::debug function (or equivalent) that I can use to disable printouts at various levels during runtime or by changing a constant.