So you will start at Narita, then go to Hakone, back to Tokyo, then Nikko round trip, Nagano, Takayama, Shirakawago and finally go to Kansai region and fly back from KIX.
I would recommend the following route.
Buy JR East Pass Nagano Niigata area (17000 yen).https://www.jreast.co.jp/e/eastpass_n/
This pass allows you to travel from Narita Airport to Odawara though you can't use Shinkansen(day1 ).http://www.hyperdia.com/en/cgi/en/search.html?dep_node=NARITA%20AIRPOR...
From Odawara, you can buy individual tickets for you Hakone travel or buy Hakone Free pass (4000 yen two days, from Odawara).
To go back to Tokyo from Odawara you can use the JR East pass (day2 of the pass).
You can use the pass to travel to JR Nikko (round trip, day 3 of the pass).
For day 4 of the pass, go to Nagano by Hokuriku Shinkansen.
To go from Nagano to Takayama, there are many ways to go, but the cheapest and practical way is to go by bus from Matsumoto. You can use the JR East pass to go from Nagano to Matsumoto.
The bus route from Matsumoto goes to Takayama and then Shirakawago and finally Kanazawa. There is a discount set of tickets called "Three Star Route Ticket" (5500 yen).http://www.alpico.co.jp/access/ticket/pdf/panf701
You can stop at Takayama and Shirakawago with this ticket and go to Kanazawa where you can catch express to Kyoto. You don't need to buy Takayama Hokuriku area tourist pass. Buy individual ticket to Kyoto (about 7000 yen).http://www.hyperdia.com/en/cgi/en/search.html?dep_node=KANAZAWA&arv_no...
In Kansai area including Kyoto, Nara etc., an IC card will suffice. Leaving from Osaka airport.
Do you mean Kansai Airport or Itami Airport?