First of all, WD-40 is not a penetrating oil, claims to the contrary by
the manufacturer and thousands of users notwithstanding.  It's a little
late now, but really, you should have used Kroil, PB Blaster, or one of
the other purpose-made penetrating oils rather than WD-40.  Guess you
will remember that next time :/

Now as to your immediate situation - that sucker is broken off in a very
difficult way.  I would personally suggest, if you have access, dropping
the downpipe so the bottom of the manifold is open, and then trying to
drill it out with successively larger drill bits.  If you are lucky the
drill bit will "catch" and spin the remaining piece out into the
manifold (this is why I suggested dropping the downpipe.)  If you are
less than lucky, you'll end up drilling it out to the threads, in which
case a spark plug thread chaser tap should clean them up.

You may find it easier to remove the manifold from the car; I haven't
ever worked on a Honda so I don't know how difficult access is vs.
manifold removal.

Needless to say, put some anti-seize on the threads of the new O2
sensor, and next time you go to replace one, before you get to the point
of breakage, try heating the manifold around the sensor with a torch,
pref. oxyacetylene if you have access to one.

good luck,

nate

Liquid Wrench penetrating oil.  Soak repeatedly.  Then pull all the
garbage out of the center of the O2 sensor that is still in the
manifold, and use an EZ OUT, or just drill the sucker with a large
drill bit until it spins off on its own.

Lg

WD 40 is $hit in a can.

yeesh. some options, in no particular order-

junkyard manifold
new manifold
new header
take it to a machine shop- let them get it out and rethread it
you drill it out/rethread it
hammer big flathead screwdriver into it, try to turn
judicious use of an air chisel, big flathead, try to turn

Might try a radial cut with a small hacksaw blade.

Soak with PB Blaster an hour. Try an EZ-Out, some tapping
(vibrations work wonders, like Michael suggests). EZ-Outs
often fail, but they often work, too. They may be had at
Autozone. Otherwise, what others said.

In my experience, PB Blaster is superior to Liquid Wrench,
by a lot. They are about the same price. PB Blaster worked
great on my exhaust system bolts last year, though the
closer I got to the manifold, the tougher freeing bolts
became.

Updates are welcome. Good luck.

HEAT. Grab a torch (MAPP or propane will work just take a bit longer)
Heat the remaining part and the manifold till it is red hot and then
spray it with some good lube(Kroil, PB Blaster or the like NOT WD40). It
will smoke like crazy. Let it cool and wipe it off. Now heat it again
and drive a tapered square style EZ OUT in good. let it set a bit and
turn it out. should come out easily this way.

If it were my car I would:
Not bother with any sort of solvent - IMO it's a waste of time.
1) Knock the center of it down into the exhaust pipe.
2) Use a hacksaw blade to saw slits into the remaining threads.
3) Knock the slit pieces into the exhaust pipe.
4) Install new O2 sensor.

I'd be tempted to forget removing it and simply drill a new hole and
tap it. I think I would be done in an hour including a trip to the
store for the tap if I didn't have one, but I do.

Wow, that can be a tuff one.

My first choice; ox-ace heat, followed by the wrench
Another option that was said to me was try to tighten first, then back out.
This tip was from a old master tech that teaches tech courses. Now I tried
it once and it didn't work for me, but we still try (I think I used heat on
that one.)
He also said ATf is a good penetrate. get the part hot and pun some on it
and let it set overnight, the dissipating heat will wick it into the
threads.
I also have in my box a tap that is the 02 sensor size, wasn't easy to find,
but I ordered it before I needed it.
There also is an heli-coil set for thread repairs, sometimes they screw
themselves up on the way out
If you remove the manifold you could carry it to a vise or a machine shop.
Heat is always the best choice.