Design a OT-based Private Set Intersection protocol to obtain $A \cap B \cap C$?
I worry that the first problem is harder than your instructor suspects. We had to work a little hard to get a multi party PSI protocol based on efficient OT in our paper


  Practical Multi-party Private Set Intersection from Symmetric-Key Techniques,  by Vladimir Kolesnikov, Naor Matania, Benny Pinkas, Mike Rosulek, Ni Trieu


If I remember correctly, we may have some optimizations for the 3-party case, but I don't think it falls to the level of a homework assignment.

The real challenge is that the 2-party equality test reveals the outcome of the comparison in the clear to one party. This makes it hard to hide partial intersections. For example, if $x \in A \cap B$ but $x\not\in C$, then Alice must not learn that Bob also has $x$. This suggests that Alice and Bob can't simply use the 2-party equality test on their inputs. In our paper we had to go to extra lengths to hide these intermediate equality test results.