Force sound's output on speakers
This is a hardware problem, unfortunately.  The problem here is that inside the port there is a "switch" that detects whether a jack is plugged in or not and depending if one is, plays audio through the jack or the internal speakers.  

The linked article talks about a malfunctining switch/port, but this isn't your case as you described; you have a stuck 3.5mm jack that won't come out so the switch is set to play audio through the port and unfortunately, there's no overriding it.

The only other options are to:


get a USB DAC (Digital Audio Converter) which is basically a USB soundcard to hook your audio/speakers up to
take the Mac in for service to have a new audio port soldered on.