If you open up an area large enough you may be able to get a spud bar underneath the linoleum. The spud bar would may work to pop those roofing nails along with everything else in one shot. Should cut the floor into sections with a circular saw. Perhaps two foot squares. You'll just have to play with it to see what works best.
Here's a real short video showing a spud bar while removing 3/8" underlayment with and engineered hardwood glued to the underlayment. Not easy work.
https://www.youtube.com/watch?v=g-hUqFzC9mk