Question
Since the leaves are falling, I've recently discovered these small green knobs on the dead-leaf stems. Some are round and quarter size, while others are oval and no larger than a kidney bean.

So I gathered a few leaves and started crackin' the knobs open. Inside, some of them had these white "pearls" that were actually liquid. I discovered that when I broke one open too quickly; it spurted out and got on my hands.

Also inside were these tiny little larva, and obviously formed insects; some were black and had wings, and others were thin and had long legs.

The knobs, I should mention, all had one tiny slit in them; an opening for them to fly out, I guess.

Breaking them open revealed a pale-green color interior, with clusters of tightly-packed larva things.

Please tell me what they are, and if I should kill them.

Answer
Livie:
You did not say what your plant was, so I will guess, based on your description that these "knobs" are a type of insect gall, called phylloxera.  We see this insect gall on cottonwood,pecan, and hickory most often. Use your computer and look in "Google Images" for phylloxera to see if the images match up with what you have.  If so, just rake up your fallen leaves just before spring and destroy them or bag them up.  The insect can overwinter inside these balls to cause a problem the following year.  They usually don't significantly impact the overall health of the tree.

Steve