headphone jack stuck in 3.5mm port, any way to force sound output via iPad Air Speakers?

Sorry, but no. You're going to have to get the headphone plug removed from the headphone jack. You can use Bluteooth speakers or headphones if you want, but to get the built in speakers to play the headphone plug will need to be removed.

Schedule an appointment at the Apple Store Genius Bar. Don't try to service the device yourself.

That is not an option. If a headphone plug is in the jack, the iPhone believes you are listening through wired headphones and you can't turn that off via an iOS setting. BTW., given the age of the iPad Air, I would run with that offer of $250 to trade up. It's only a matter of time before support for that device ends altogether.

The "port" you refer to is a headphone jack. What was forced into it is called a "plug." Assuming the plug has not closed the connection to the headphones, then you can route music via Blue Tooth to a set of BT speakers or BT headphones.

Make an appointment at the Apple Genius Bar for service. If you need to find an Apple Store - Find a Store - Apple. Also, see How to find your nearest Apple Authorized Service Provider (AASP) or Distributor (AAD). 

"Your Apple-branded or Beats-branded hardware product (“Product”) is warranted against defects in materials and workmanship for a period of ONE (1) YEAR from the date of original retail purchase (“Warranty Period”) when used in accordance with Apple`s user manuals (refer to www.apple.com/support/country). Under this warranty, you will be able to direct your claims to Apple even in situations where you purchased the Apple Product from a third party.” [Apple One (1) Year Limited Warranty – Accessory - For Apple and Beats Branded Products Only.]

Try using the lighting port. Works on my iPad.

An Out of warranty repair/iPad replacements, for something major, other than a diagnosed battery replacement, is approx. 60% of the particular iPad model’s original cost.

I have been to the genius bar and they were unable to fix it. They offered me a $250 replacement for my old iPad Air, which I didn't want.

Care to tell me which Apple store you went to? I have an iPad Air 1st gen too. It's the 64GB cellular + WiFi model. I'd grab that $250 instantly and trade up. I understand that offer does not necessarily apply to all Apple stores. Still worth a shot if the store is in the same city I live in.

@ Rbrylawski and Shag CA.

You guys got this all wrong and misunderstood, I think.

The Apple Store isn't offering the OP $250 for his iPad Air toward a new device.

Apple is going to charge the OP $250 for an out-of-warranty replacement iPad, with an identical iPad Air model.

BIG DIFFERENCE THERE!

I knew what rbrylawski posted wasns’t accurate.

Just so I know for future reference, but will that work on an iPad which still has a dedicated headphone jack?

Yes does on mine. Was surprised when I tried it. But you cannot use both to with two separate headphones. One will cut off.

Good to know thanks.

I had to re-read OP's posts and I think you are correct.

Welp, didn't I maybe get it wrong. I too reread the post and MichelPM, I do believe you read it better than I did.