Overhead lifts with zero core and lower body movement with no jerk is one of my most challenging lifts. It is all arms and shoulder strength. When it gets heavy i really lose my ability to explode from a clean to straight arms up in the air. I am pressing 150 today as my max. For overhead lifts, you definitely hit a wall in a matter of only 2.5-5 lb increase.

The reason why I am writing this thread is I need some advice on how to get stronger faster so I can lift much more for a max. If I am going to transition into the Olympic lifts soon, I better be able to do the overhead lifts with heavy weights.

I have found that doing military presses and full dive bombers really helps with strengthening my shoulders and upper region so far, especially when reversing the motion. However, my weight is 177 and not all of it is on my hands when doing these body weight exercises. I suppose handstand push-ups would be a better exercise to improve overhead strength, but I am not ready to do these yet.

For reference, here is a description of a full dive bomber (great exercise) :

http://www.fitnessmagazine.com/workout/arms/exercises/dive-bomber-push-up/

Is building up my pectorals from bench pressing or doing pushup variations going to help with overheads? My upper body strength in chest and back are the strongest in my body followed by upper legs.

What suggestions do you have?

Triceps dips using a bench as well as a machine for this to do hanging body as you can. They'll help with shoulders and upper part of chest as well as triceps. Compound movements for your entire upper body will help. Shoulder shrugs, upright rows and yes, back and chest strengthening will help too. Entire core needs to be strong to increase this kind of movement.

edit - make sure you're working with negative reps as well. This will show good gains in strength using your current weights.