Why does the B-52 outboard engine nacelle have a sharp change in shape?
The B-52 was build in different versions (A-H) and the engines and their installation differ between these version1.



The image in the question most likely shows the engine configuration of a B-52H.

The following drawings suggest that this also changed the inlet design2.



There seem to be different engine-designations depending on the application. For the B-52H, JT3Ds (TF33-P-3) were used3.

Pictures of the TF33-P-3 inlet show they are symmetrical. (While the question is focused at the outboard engine-inlet, this question can only be answered taking the other engine and the placement relative to the wing into account as well).



At the symmetry-plane the TF33-P-3 inlet-section extends further than the rest of the inlet-lip.

I would guess that there are multiple reasons and considerations which led to this design. Three of which will most likely have been:


Basic aerodynamic considerations like stagnation-point and pressure distribution will prefer a sharp/point nose over a flat area. Especially since the air needs to be diverted from the engine-pylon.
The cruise speed of the B-52H is Mach 0.914 which means the nose could also be some kind of anti-shock-body reducing wave-drag by applying the area-rule.
The nose between the two engines prevents aerodynamic interaction of the two engines, for example during cross-wind operation.


The negative aspects of placing two jet-engines close to each other were also discussed in another SE-question with respect to commercial airliners.



[1]:www.airpowerstrategy.com/
[2]:http://www.afwing.com/
[3]:en.wikipedia.org/wiki/Pratt_%26_Whitney_JT3D
[4]:www.globalsecurity.org/wmd/systems/b-52.htm