Chosen Solution
I pushed mini jack into headphone port and lost headphones and internal audio
It is possible to replace the audio jack, but there is no iFixit guide at this time for it for this machine. However there is a guide on a similar iMac machine that has the same display size, if you are willing to take chances and see if they are at all similar because I have never worked on this particular model of the iMac. Do it at your own risk!
Did the tip of the headphone jack get stuck inside? If it did you could try this tool GripStick Headphone Plug Extraction Tool.
