I have seen two sources (one was LA Times) state that new members are not sworn in until after a speaker is elected. If that is correct, how do the results of an election get reflected in that key election?
Ch. 34 of House Practice: A Guide to the Rules, Precedents and Procedures of the House explains that "The general practice for election of Speaker begins with nominations from each party caucus followed by a viva voce vote of the Members-elect". We know who those people are; one of these days, they may make the transition to being "Members", after the Speaker is chosen and sworn in.
2 USC 25 says that after elections,
the oath of office shall be administered by any Member of the House of Representatives to the Speaker; and by the Speaker to all the Members and Delegates present, and to the Clerk, previous to entering on any other business; and to the Members and Delegates who afterward appear, previous to their taking their seats.
It is up to the House to decide if "and" means "and after that".