Dear Dianne,
Welcome to the forum.
Glad to hear you are returning to Japan. There are no JR lines to Sumoto, Awajishima or anywhere close. The only access option I found was by express bus.
The time table can be found here:
http://www.awaji-kotsu.co.jp/news/upload_files/%E6%B7%A1%E8%B7%AF%EF%BD%A5%E5%BE%B3%E5%B3%B6%E7%B7%9A%2829.4.1%29.pdf
and is available in Japanese only I'm afraid. Here are the Kanji to help you.
徳島 = Tokushima and
洲本高速BC is Sumoto bus station.
The time tables on the left are for week days while on the left for weekends and public holidays. The time tables on top are from Sumoto to Tokushima and on the bottom from Tokushima to Sumoto. I think the fare comes out at 1,300yen/one way/person.
Then from Sumoto you can use a bus to Sannomiya in Kobe and use the JR from there to Osaka.
You can find the details for that bus here in English:
http://www.shinkibus.co.jp.e.rz.hp.transer.com/highway/category/route_guidance/kobe_sumoto.html
Hope this helps,
Daniel