damaged subfloor

First, the hole for the flange was cut too big and the flange is not all that secure to the floor. Now the toilet seems to be sinking/leaning.

I'm ready to repair it, but would like to tear up as little as possible.
What is the minimum amount of floor I can cut out and replace and still be solid. Do I need to span a certain number of floor joists? New flooring will be linoleum of some kind. Needing to keep the costs as low as possible.
What am I facing here?

 

Replacing a larger chunk of floor is not much more work, and in fact may end up being less work, than trying to piece in a very small patch.
One technique is to add some sister joists to attach a patch piece to. If you don't do this, then you have to get the old subfloor cut right on the centerline of a joist so a patch can share. This is tedious. Better to cut out a little more subfloor, and use the sister joist technique.

Sheet flooring requires an absolutely smooth substrate. You will have to either go over the entire floor with some 1/8" or 1/4" luan, or carefully feather all subfloor seams with leveling compound. Probabaly both.

 

Thanks for the info.