That is a neat freeWHEEL that has removable/replaceable cogs. I've never seen one like that in person.
The standard technique is to use the shimano freewheel spline driver tool, and a big 12" or larger adjustable spanner. That's enough about a third of the time
In my experience, the reliable technique is to go straight to a well-mounted bench vise. Clamp the tool in the vise so the splines point upward, lower the wheel down so the splines engage, and then use the full diameter of the rim as leverage. It will unscrew anticlockwise when viewed from above.
It can help to imagine you're trying to spin a large heavy barrel which is on it's end. As for being stuck, this unit has been tightened every time you push a pedal, so yes it will be quite tight.
I've never had the vise trick fail, but its possible there's corrosion and galling in the threads, so some penetrating oil might help too.
It may be hard to find replacement cogs, so you might choose to buy a common freewheel for daily use, and store this weird old one for a future rebuild.