Unfortunately the answer is that there is nothing you can do to extend your current stay.
What's more, as you've overstayed your allowed 90 days, your current ESTA is now invalid, and you will likely not be approved if you attempt to apply for another one. If you attempt to re-enter the US with your current ESTA you WILL be denied entry.
Your odds of being able to obtain a visa in the near future are also low. If you have overstayed by more than 180 days then you will be automatically banned from the US for 3 years. If you've overstayed by more than 1 year, the automatic ban is 10 years.
At this point I would suggest leaving the US as soon as possible to minimize the period of your overstay, but one way or another your chances of obtaining a work visa for the US in the near future are somewhere between extremely low and zero.