Broken oil shaft

Use 15 min lock tite and glue something like a 1/4 bolt to the end of it to pull it out with.
The 1/4 bolt threads will be good for the glue to get a grip on.
I'd give it a lttle more than 15 min to set though (half hour would do it)
Just clean the oil off the end of it first.

I use that stuff all the time for oddball crap like that.