What is straight line black box reduction? I understand the notion of black box reduction. But what is straight line black box reduction?
A straight-line black-box reduction is one that interacts with the adversary in a black-box manner (read: is given oracle access to the adversary) and "cannot rewind" the adversary. 

So, assuming (as an example) that the protocol has the corrupted party receiving $5$ messages, then the straight-line black-box reduction can/will give the adversary the messages $m_1,m_2,m_3,m_4,m_5$. In that order; and in that order only. 

Simpler said: a straight-line black-box reduction interacts with the adversary the same way it interacts with a regular party.