Ahaz is the king of Judah, Rezin is king of Syria, Pekah is the king of Israel (also called Ephraim in the chapter). Israel and Syria formed an alliance and attacked Judah, but were unsuccessful. See 2 Kings 16:5 for a similar account.
The wording is a little hard to read. The prophet is basically saying, "Something far worse is coming … the Assyrians." "even the king of Assyria" is meant for dramatic emphasis.
Isaiah is describing what life will be like for the Israelites when the Assyrians come. They will be everywhere (v19), the natives will be removed – foreigners are providing services (20). They will live and and eat simply (21-22). You've never seen anything like what is coming (17).