Subfloor repair

I posted this pic quite some time ago showing rot around my toilet from
below.

I have now removed the toilet, a layer of tile, a layer of vinyl
flooring and the two layers of underlayment that were accociated with
the flooring.

I cut the rot out and now have one problem and that is supporting the
new subfloor I must install.

On the west side the tounge is available so that will not be a problem.
For the north, I plan to cut back to the floor joist or alternatively
cut even with the joist and add a sister to the floor joist to make
things easy for myself.
On the east, I will add a 2x4 to connect the floor joists and use that
for support.

That leaves the south... it is an outer wall and the floor joist is 6
inches in (beyond the floor I have cut out. I can only think of two
options (since there is plumbing in the way to make things worse....
(1) Add a hanger 6 inches in between the two joists, then put in a
crosser of some kind... or (2) screw some thick plywood to the bottom
of the existing subfloor and use that for support.

Any advice or other options?

NSWE without references confused me. I am assuming that your problem is
with the area where the toilet supply line is. Other than the wall sitting
on it, I can not see that area getting a lot of traffic. If you can figure
out a way to properly support a 2x4 under the cut edge of the osb it will
support the minimal load you need supported. Use a joist hanger at 1 PM
position and the 8 PM position and run the 2x along that axis.

My answer is as confusing as your question.

Here 2000 words. Add 2x4 or better where the red lines are.

I would add the extra cross bracing under the toilet flange also.