You need to read up on mask modes and mattes and how to use them to mutually cut and slice shapes using duplicates of layers and then reassemble everything. The same would apply to shape layers and their various ways of working with groups and additional operators. Assymetrical deformations can easily be created e.g. using a Bezier Warp or Mesh Warp effect and of course when working with shape and mask paths by selecting the respective anchor points only. Inserting additional points may sometimes be necessary to get something to work with. In any case, you need to get away from trying to do everything at once in a single comp. Creating most elements as separate pre-compositions and then using them will eliminate a lot of headache. E.g. you would create the various cross-sections as "clean", symmetrical shapes in the pre-comps and then in the parent comp apply effects tu push and squeeze them and adapt them to the curvature of the eyeball and incidentally also this way being able to animate e.g. pupil dilation or lens adaptation.
My apologies, however I do not understand 80% of what you are saying. You said that I should read up on mask modes and mattes, may I receive a link for it?
Secondly, Would the technique you have stated work for an image? and I got really confused when you started to mention about "Assymetrical deformations".
I'm sorry again but I am very new to adobe after effects. Perhaps you can explain your words in a more simple style?
If you're new to AE and what he's saying isn't making sense, you would greatly benefit from going through this first. AE is much too complicated to just try diving into it. It's not like Photoshop or Premiere Pro!