Hello!
With all due respect, I disagree. If you take a tiny styrene rod and drill inside, you have a good chance to create a weak spot, that can break again. My solution would be to just use the right styrene glue, and just glue the parts together along the broken spot. We're talking here about welding the parts together, using acetone, MEK, or mixture of those and similar substances. If the surfaces are clean, the joint should be every bit as strong, as the original part. Unfortunately messing with epoxy, CA or other stuff contaminates the surfaces and afterwards it's hard to restore them so that the glued part is straight and right length. And I'm talking here about a tried method - thet's the way I do it.
Hope it helps, have a nice day
Paweł