Old iPhone still accepts calls

I'll take a shot at it. Someone else can pipe in and verify and/or correct if necessary.

If I had to guess, the calls you have 'Coming In' are from other iPhone Users. Your Apple ID is likely still also associated with the old iPhone. Therefore, iPhone to iPhone calls will still work as long as the old phone has a wireless connection (your home's wi-fi as an example). In this manner, the old iPhone would receive calls even though it is not connected to a carrier's network.

Now, as far as fixing it. It's been awhile since I had to do it, but if memory serves me correctly, it can be a pain in the butt, but most certainly can be done.

I would suggest going into the settings of the old phone and doing one of the following...

- Remove your Apple ID completely by resetting the device (Make sure to back up first!)
- Or, you can probably just reconfigure Face time in the settings (Old Phone) to not answer those calls by changing the email address it is associated with. (Also in settings)

If it is not iPhone to iPhone (Face Time calls) that you are receiving then I'm not sure what the next action would be currently.

I know from past experience that Apple kinda holds your Apple ID 'Hostage' if you will, and it can really be trying to get the calls routed to the right device. Basically, Apple ties your Cell Phone Number to your Apple ID. This definitely caused issues going from an iPhone to an Android with regards to calls and messages.
I know that sounds confusing, But unless they've fixed things, it can cause issues like you are describing.

Anyway, sorry for the wall of text. Hope maybe it at least points in the right direction!

Thank you.

Just to piggy back on what everyone else is saying. This is part of the Apple "hand-off" feature. Basically the same if you received a call on your Mac, your old iPhone has pretty much become an iPod Touch. He can probably only receive the calls when he's on WiFi.