How do I dry out a damp patch in my subfloor?
You say, "The tar paper between the subfloor and hardwood was also damp."  I don't see the "tar paper". You MUST have a moisture barrier. 

However, your question is about drying the area out. I agree with @isherwood, keep a fan blowing on it and it will dry out faster. However, be aware that the rapid drying could warp the oak flooring. To minimize this problem, I'd re-assemble the oak boards to keep the boards straight. 

Btw, I'm surprised I don't see "damaged" edges along the edges of the oak flooring from being nailed in place. 

Also, I thought this type of floor needed to be installed on "sleepers".