This answer on the ELL SE says that "give a party" is interchangeable with "throw/hold a party:"
What is the difference between "hold a party", "have a party", "give a party" and "throw a party"?
I think they're all pretty much interchangeable.
Everyone on this forum thread takes the phrase in stride:
You might give a formal tea party, but you would not throw a formal tea party - even if you were discussing it informally.
I haven't heard "give a party" used before. Is it regional (or have I just missed it somehow)? If so, where's it most used? (I'm in Colorado)