Hi there!
In order for a 7 day pass to be worthwhile you need to spend more than ¥28,300 on JR tickets. Lets look at a breakdown of your costs for the travel you list so far:
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Kansai airport > Osaka: ¥2,600 (53mins, 57km)
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Osaka > Kyoto: ¥540 (29mins, 42km)
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Kyoto > Odawara: ¥11,950 (177mins, 429km)
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Odawara > Tokyo: ¥1,450 (36mins, 83km)
JR ticket cost: ¥16,540 for 4 legs
As you can see, you need to spend another ¥11,760 on JR travel for a 7 day rail pass to be worthwhile. The Japan Rail Pass would certainly be worthwhile if you were to do more travel, such as a return to Nikko while you are in Tokyo, or a return to Hiroshima while you are in Osaka, however as it currently stands I think you are unlikely to do enough travel on the JR system in Tokyo for the pass to be the right choice.
If you did decide to do lots of day trips from Tokyo, it may be worth starting a JR Pass from your trip up to Odawara/Hakone and then use the pass all the way up until your leaving day from Narita - it does depend on your itinerary though.
You can look up more precise train timetables and costs at the Hyperdia travel planning website and learn how to use Hyperdia for JR Pass holders through our video blog.
JR Pass in Kyoto and Tokyo
The JR Pass has limited use inside Kyoto as most travel is via the municipal metro and bus lines. Within Tokyo you can get good use of the JR Pass on the many JR lines throughout the city however you will possibly want to look at the non-JR metro travel to certain locations.
Student price for JR Pass
I'm afraid that as the JR Pass is already a heavily discounted ticket there are no discounts available for students.
Hope this helps!
