"strong bench press weak pushups"

If this is you, bad news bears. This indicates to me that you lack strength in various stabilizer muscles that are needed to bring your bench press to new heights. Bench press does not work out the stabilizer muscles, back, and abdomen, but push-ups with good form will work a large portion of your body.

Although you lay on the bench, various stabilizer muscles are still needed for you to achieve maximum bench press poundage.

prescription: just do push-ups

trouble locking out the bench press

This indicates weak triceps, end of story.

prescription: diamond pushups - similar to close grip bench press, but for pushups! (put palms of hands on ground and touch the thumbs and index fingers of both hands together)

alternatively: handstand pushups (for the record I can only do them in poor form against a wall)

signs of a plateau on bench press

If you're hitting a plateau in your training, that's both a bad and a good thing in my opinion. It's good because it means you've hit your stride, and you can now handle a good bit more than you were used to before. However, it indicates complacency. It is very easy to become complacent in your strength-training activities.

prescription: CLAP-PUSHUPS! (push-ups in which you forcefully push yourself off the ground and clap your hands together before catching yourself)

Although Plyometric exercises shouldn't be performed by most people, if you're plateaued on the bench press (or any exercise) performing a plyometric version of that exercise (with appropriate resistance of course!) will help you break through the plateau. Explosive exercises increase the ability of your nervous system to recruit fast-twitch muscle fibers, and they provide a new form of resistance curve that your muscles have to deal with.

The traditional method of breaking through a plateau is one that simply involves willpower - you force your way through it. Although this can be effective, it is often a woefully inefficient method. You have to remember that your body and mind are ridiculously lazy contraptions, and will only adapt when forced to do so. You can either force your body to change with sheer effort, or you can provide it with unexpected, changing conditions that force it to adapt.

Although strength training is about increasing the weight (resistance) you can work with, oftentimes you need to provide yourself with the path of least resistance.

difficulty with initial move off the chest

This is my main problem. This is large a function of weak pectoral muscles. If this were an article about how to simply increase your bench press by any means, I would recommend that you perform decline bench-presses or bench presses with an extra wide grip in order to increase the strength of your pectoral muscles.

However, I am writing about how to increase your bench press using only push ups, so that's cheating. Also, I do not currently have a bench in my apartment, nor would one fit, so I am in the same boat as anyone else that wants to increase their bench press with just push ups.

The way I have been approaching the problem lately is by performing wide-arm pushups where I focus only on the lower part of the push-up range, as this is the part of the motion that most intensely recruits the pectoral muscles.

In order to increase the workload (push-ups for the moderately physically fit are a relatively low-impact exercise) I elevate my hands on top of a couple pairs of two-by-fours. Increasing the range of motion of an exercise increases the force required to perform that exercise. Combined with a wide-grip pushup where I only focus on the on the specific range of motion that recruits the pectorals, this approach has been effective.

Specifically, the range of motion that I am discussing is where the widest angle the elbow forms while doing the push-up is not much greater than ninety-degrees, and using the extended range of motion that the two-by-fours (or books or whatever) allows for a very acute elbow angle to be achieved at the bottom of the motion (my nose is touching the floor at this point). Assuming you have maintained good form throughout the push-up, the pectoral muscles will be recruited in a very effective manner.

if you're too strong for any of these push-up tips...

Get someone to sit on you, purchase a weight vest to do push-ups with, or maybe even learn how to use resistance bands to increase the resistance that your push-ups provide.

good luck!