It might be helpful to ponder exercises 6/7 in the notes. Specifically:

• Show that there is an oracle A and a language $L \in NP^A$ such that L is not polynomial-time reducible to 3SAT even when the machine computing the reduction is allowed access to A
• Suppose we pick a random language B, by deciding for each string independently and with probability 1/2 whether or not it is in B. Show that with high probability $P^B \ne NP^B$