Here is one way to at least get you started:
In "Departing from" put CPH :: HEL LON BA1-4 JFK PHX
In "Destination" put OGG :: PHX JFK BA1-4 LON HEL
The double colons ("::") will do the work of putting the routing options into the "Advanced Routing Codes " fields
This basically means fly from CPH then to HEL then to LON (covers all London airports) then on one of BA1,2,3,4 to JFK then to PHX then to OGG. Similar for the reverse. Use the calendar option and start with a date in the allowed ranges (see post by KARFA).
Once it brings up some flights you will have the flight numbers and booking (fare) codes to tell the agent when you call up to book.