Oil spray residue in engine compartement

There shouldn't be much spray from a dip stick tube, so look for some other cause. Typically when the handle breaks off, the rubber seal remains on the stick in the tube, not on the handle part. If the stick is close to the top where you can see it, you may be able to drill a hole in the plastic and run in a threaded wood screw that you can pull out with a needle-nose pliers. Be careful to not push the stick down further. You can also spray both parts with carburetor cleaner or brake parts cleaner, then glue the handle back onto the stick with epoxy. That isn't a fix. That's a way to get the stick out so you can replace it. Make a tube out of paper and slide that into the tube first so the glue won't stick to it.