Trip odometer doesn't reset when you push the button. Actually, the button doesn't even go in and has a sharp screw side to it. Would like to have a working trip odo, how do I fix this?

The trip odometer doesn't reset by just pushing in on the reset knob like newer cars. You have to push in and then keep turning the knob clockwise to rotate the numbers on the trip odometer until they all get back to zero.

...and has a sharp screw side to it
I think maybe you are missing the reset knob?

Does it look like this:
http://elcaminocentral.com/users/elcamino/pics/reset_knob.jpg

or this:
http://elcaminocentral.com/users/elcamino/pics/reset_knob_missing.jpg

Choice B. Missing the reset knob. Where can I get one?

Where can I get one?
Go to your local GM dealer and order the universal knob kit. It's GM part # 14053344. It'll cost you about $7-8. You may have to paint it black to match. Or, you could go to your local junkyard and hunt one down. If you choose the latter make sure you bring a very tiny screwdriver to remove the center screw. See the above picture.

Was good to hear that pushing the lever does NOT cause the odo to go back to zero. Thot mine was defective.

On a related topic, when installing white gauge overlays recently, I attempted to clean and lube the trip odo as mine will go back to zero, but goes to 111 on the first mile. Any ideas on where I might look for a problem and/or how to make it work properly? Thx!