Are there some push-up variations I can do to work the biceps or shoulder muscles? Illustrations or pictures would be appreciated as well.
Livestrong.com has a great article about variations in push ups:
To work your shoulders you can increase the elevation of your feet. If you can, you could do handstand pushups against a wall.
Push-ups do not really target biceps. You probably want pullups for that.
These probably aren't really push-ups in the traditional sense. They're more like a hybrid between a push-up and a pull-up. They have the benefits of a push-up as in they target your core, chest, and shoulders. With the added benefit of a pull-up because they also target your upper back, lats, and biceps.
Note: Using a swiss ball to increase resistance (difficulty) is completely optional (and pretty hard core), it's only included here for lack of a better picture that demonstrated the full movement.
An easier variation is to do them with your knees bent and feet flat on the ground.
There are many more variations, but these should keep you busy for a while!
There sure are, check out this article - 7 Muscle Targetting Push Up Variations
I'm a big fan of Exrx site, you can browse this site based on which muscles and which body weight form to work.
I'll summarize some exercises to work the shoulder muscles here based on both of my favourite sites:
And some exercises to work the biceps here:
I am a big fan of fingertip pushups:
They seem to build the biceps more than standard pushups, and they build hand, finger, and forearm strength as well.