That's a manual log loader from the "Workin' on the Railroad" sets of the late 70's, I believe. (origins could have been Marx, I suppose - I don't know the history to say it's not). I do recall there being PC stickers, but those do look larger than what I remember coming with the set.
Might have been in other sets too.
The slot in the back wall had a small manual lever with a curved "catch" that would hold a log you slide in from the side (one at a time) until you released it by gently pushing the lever down. That piece seems to not be present in your pile. I think you may be missing some other pieces, possibly the platform where the logs slide into the square opening in the side, as shown on the set box (see link below).
I forget exactly how the other pieces go together, but the piece with the "prongs" is I'm pretty sure mounted at an angle in some way near the long rectangular opening so the logs would roll out along the 3 extended prongs into a waiting log car (which was also manual - you would "rock" the part the logs rest in to dump to the side of the track). The squarish piece with the "X" cross pieces that sits on your table at an angle (nearest your oven door in the 3rd photo) is the "tray" you would dump the logs into from the car.
If it was in front of me, the six year old that still lives inside of my consciousness somewhere might remember exactly how to assemble it, but I'm not typing my thoughts very well!
Here is a link including a picture of the set box for the one I had in ~1978.
-Dave