I finally discovered and learnt
Blender shape keys:

(actual render 320x240, too big to upload. Underlying shape being animated is a simple box with a subsurf modifier on it)
This is.. ASTONISHINGLY easy, not to mention really fun.
* Select the object you want to animate.
* Go to the object data panel (looks like a wireframe triangle with highlighted vertices) and hit the 'plus' button to add the 'basis' key
* And hit it again (with the 'basis' key selected) to add a key relative to the basis key (this will be called 'Key 1' for now).
* Turn up the 'Value' slider on Key 1 to 1.0 (so that you can see the changes you're making)
* Enter Edit mode (Tab key).
* Move/rotate/etc vertices til you arrive at a shape you like. Exit edit mode.
Then:
* You can adjust the 'Value' slider for any key to interpolate between it and the base object
* This works for all keys at once, so you can mix amounts of different shapes in (this is how I got the range of sproings and twitches-- mixing 2 or more keys)
* You can animate these shape changes by inserting keyframes for the Value slider on the relevant Shape keys.
That's my recap of what I learnt.
I also just discovered that you can apply keys inversely (set Min to a negative value, then adjust Value below zero) and/or at a greater magnitude than 100% of the change (set Max/Min to a higher/lower value, then adjust Value). That's neat for crazy effects.