Hi Matt,
hmmm, good questions!
Firstly, yes, you can use the JR Pass on main line trains and also smaller local JR services. Note that the JR Pass is for JR lines, and can not be used on the subway. That said, it will be find for all of the locations you mention in your list, and can also be used well on all JR lines in Tokyo.
As I understand it, you plan on using a 7 day pass from the 18th to the 24th. Firstly, lets take a look at the base JR ticket costs to see how they compare to the 7 day pass:
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Osaka > Okayama: ¥5,860 (68mins, 184km)
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Okayama > Kobe(hyogo): ¥5,440 (60mins, 143km)
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Kobe(hyogo) > Osaka: ¥390 (25mins, 33km)
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Osaka > Nara: ¥780 (59mins, 48km)
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Nara > Tokyo: ¥13,750 (227mins, 555km)
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Tokyo > Otsuki: ¥2,860 (85mins, 87km)
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Otsuki > Tokyo: ¥2,860 (76mins, 87km)
JR ticket cost: ¥31,940 for 7 legs
As you can see you'll make small savings with the 7 day rail pass and also retain flexibility to change plans as needed (travel to Hiroshima, Kinosaki onsen, or Nikko for example all make good extra day trips which will be free during your validity period). Note that I have not included travel to the airport (If Narita, add a further ¥3000 savings) and travel on JR lines around Tokyo (¥200 per trip).
Hope this helps!