Typically, how many crew (pilot and cabin) would fly on an ultra long distant flight such as one from Newark to Hong Kong (let’s take United as an example)?

Most likely 4 pilots—a Captain and First Officer, and a Relief Captain and Relief First Officer.

The primary Captain/FO would do the takeoffs and landings, and the Relief crew would fly inflight. Most likely a flight of this length would be 2 shifts each, with each crew taking two breaks in the bunk, around 3-4 hours each.

Similar for the Flight Attendants. The size of the cabin crew would depend on the size of the airplane. An extra FA (or 2 or 3) would be added as the flight time increased as well. The cabin crew would then schedule crew rest breaks similar to the way the flight deck crew would.

Below: My happy crew (me on the Right), off for our JFK-DEL flight!