There's not much on during those dates you posted, SuperGT is at Sepang then and Super Taikyu, D1SL, MSC, JDDA drags etc all falling outside those dates.
Okayama circuit is fairly easy to get to, and on the days they have big events there's usually a shuttle bus from the closest station to the circuit called "JR Yoshinaga" (JR Okayama station is past JR Yoshinaga by quite a distance so don't go to JR Okayama by shinkansen if you can help it, you'll just be doubling back).
JR Yoshinaga google map
You can get a train from Osaka (Umeda) or Kobe that goes out to Himeji but you'll have to change trains to a local one to get to JR Yoshinaga. It's fairly easy though and if you have trouble just wave a map with Okayama circuit on it at any station I'm sure the staff will help you out. The shuttle bus from JR Yoshinaga to the circuit may or may not be running so you might be up for a 15 - 20 minute taxi ride. If so keep the map handy because you'll need it to explain to the non-English speaking driver where you want to go... Yoshinaga is about as small as towns get.