Cast iron cookware restoration
You have 2 options to remove varnish at home:


Mechanical removal by sanding or scraping by hand or using a rotary tool. If you are too aggressive with this you could damage the pan, but if it is done right you will get a lot off. This could be tricky because of the shape of the pan, all of the curves and few flat spots, hand sanding will probably give you the best results in the curved parts 
Solvents like varnish remover dissolve varnish and lacquer chemically, allowing you to wipe it off


Personally I would do both: start with my dremel and see what I can get off with a fine grinder attachment, and see how it comes off with sandpaper and a bit of elbow grease, then I'd use a varnish remover to get off the rest. Make sure you don't do this in an enclosed space and have good ventilation when you use the solvents. Eye protection is important, you don't want to get a fragment of varnish in your eye, trust me on this.  

I have left out media blasting (sandblasting or glass bead blasting) as an option because it would probably cost more than buying a new pan, but if you know anyone with a machine it would make short work of it without chemicals. 

Whatever method you use make sure to season it straight after, or at least heat it and run it down with oil to prevent rust.