The flange should sit on top of the finished floor, if it doesn't you'll have to modify the plumbing or find another way to achieve this.

Notice in this image how the toilet waste pipe sits just inside the flange opening, this is the proper way for a toilet to sit on a flange. Even without a wax ring, this union is not likely to leak under normal circumstances (I'm not recommending a wax ring not be used).

Wax as a waste pipe?

Some folks recommend using a thicker wax ring, or even doubling up wax rings. The problem with this, is that you end up with a waste pipe made from wax. Now this might hold up, but more than likely it's eventually going to fail, and leak.

Modify the plumbing

If you have access to the flange from below, you might be able to modify the plumbing to make the flange sit atop the floor. In most cases, however, this is not an option.

Adapters

There are adapters available, that solve this exact problem. The Set-Rite Toilet Flange Extender Kit; described in the answers to this question, Comes with different size spacers, which allows it to compensate for various sized offsets.

I'm betting that whomever installed it last used an adhesive to secure and seal the toilet to the closet flange and/or the floor. It sounds as if you are renovating so unless the toilet has value (or fond memories) break it out with long handled sledge hammers (use eye protection). The time saved by not solving a mad scientist monstrosity might be worth the cost of a mid-priced new toilet.