What is the best way to pick up self stick vinyl tiles?

Warm up the tiles to soften and melt the glue. A hairdryer works. A heat gun releases too many fumes from the linoleum.

I start with heating the edge and pulling it up with a wide flat thin crow bar. Loosen the entire edge edge and then use a narrow flat shovel with a handle to pry it away from the plywood. A razor knife to cut some of the chunks smaller helps too.

Wear gloves and a mask if the area is dirty and get the area as clean as possible. Residual glue usually isn't a problem on the plywood because you'll cover it with an underlayment.

There is is a tool that has a sharp edge and cuts between glued carpet or linoleum and the floor that can be rented from a rent all or big box store. I haven't used one because demo is a nice workout.

Personally, I would just cut the subfloor (plywood) with a saw and pry it up in sections to remove. Then put in a new subfloor and flooring. But to remove glued down vinyl, a heat gun and a long-handled scraper is the equipment to remove vinyl and lots and lots of elbow grease. Don't envy you..... better check the vinyl for asbestos cause that might be the reason they just put new flooring on top. If it is asbestos, you can't remove it .... this is the reason many contractors just cut out the floor and replace it.

Holy moly. First do you know if original layer has asbestosis? Get that checked out first and foremost cause with that many layers you may have that.

Elbow grease and a good strong putty knife a spray bottle of rubbing alcohol will also help with the stickiness