If you want strength, then instead of going for a high number of reps, fill a backpack with heavy books (or whatever heavy object you choose) until you can only do 5-12 pullups/pushups with the given weight.
Gradually build up the weight as you get stronger.
If you insist on using your body weight, then try doing handstand push ups against a wall or one arm pullups (great for bicep definition as well).
By going until failure you're predominantly building your endurance, not strength.
BTW the plank is relatively useless if you maintain proper form while doing pushups.