The layers are as follows:
Vinyl
particle board
linoleum 1 stapled into the floor
linoleum 2 directly under linoleum 1, possibly glued together
thin substrate -- unknown composition glued to hardwood flooring
green glue layer.

We were able to easily remove the staples with channel lock pliers but a few broke off all the way down to the hardwood flooring level.

We used the sharp end of crowbars to remove the layers down to the thin substrate. Most of the substrate comes off using the same technique with the crowbars but will also require some chiseling.

The whole point of this is to get to the hardwood floor so we can have it professionally sanded and finished. At that point, the kitchen floor will be integrated with the rest of the house.

I'll try to get some pictures up so you can see what I'm talking about.

Burt