If two black hole mergers happen close enough would there be any interesting effects due to their waves constructive and destructively interfering? If two pairs of black holes were to merge at the same time in the same plane within close proximity (small odds) what effects could be observed due to their waves constructively and destructively interfering? 
Would there be gravity wells with no matter? What else may be observed?

 A: In principle, colliding gravitational waves, if strong enough, can be focused by nonlinear effects from their mutual interference so strongly that  a singularity is formed surrounded by a horizon, and the end result is a black hole flying away from such collision. See, for example:

Yurtsever, U. (1988). Singularities in the collisions of almost-plane gravitational waves. Physical Review D, 38(6), 1731, doi (paywalled).

However whether such strong interference could be formed by two nearby black hole collision in such a way that new resulting black hole would not be immediately swallowed by one or both of the black holes from the mergers is a different question.
Additionally collision of gravitational waves may have quantum effects: production of photons (and other particles) of almost thermal spectrum (analogous to Hawking radiation), see for example:

Dorca, M., & Verdaguer, E. (1993). Quantum fields interacting with colliding plane waves: particle creation. Nuclear Physics B, 403(3), 770-808, doi (paywalled).

From a philosophical viewpoint such process is quite remarkable: "matter" created from "empty" spacetime. However the temperature for such created radiation for astrophysically realistic black holes would be too low for detection.
