So there are several audio related things I do with my phone (which is not iOS) that I do while at my computer, and it'd be grand if I could play my podcasts or take my softphone calls on it. Is it possible with Bluetooth, or any other wireless method?
I don't know of any one OS X app that can do all of that for you, but here are a few recommendations.
Turn your Mac into an AirPlay Speaker
Airfoil from Rouge Amoeba works great for me to stream podcasts, music, radio, etc. from iOS devices to my MacBook Pro (Mid 2012). Note that you'll need to also install Airfoil Speakers which is a free, separate download (scroll down to "Airfoil Speakers for Mac"). The separate Speakers download requires the purchase of Airfoil, even though the download is free - think of it as an add-on to Airfoil even though it runs as a separate app. Further note that AirPlay is a one-way transmission and cannot be used as a speakerphone. See the next section...
Turn your Mac into a Speakerphone
Not sure what kind of softphone you have but check with your IT or phone system admin to see if there's a Mac client available. If there is, you'll also need configuration details from them so ask for that too (or have them set it up).
There are a couple of OS X apps that allow you to control your iPhone (and a few other types of phones) via Bluetooth but I've not had good luck with the reliability so I didn't purchase. I can't advise on those but a search online will turn up a few options if you'd like to try your luck. They've been around for awhile and are still under active development as far as I know.
I tried pairing an Android (4.2.x) phone (Alcatel One Touch Idol X) to a MBP: no love.
I couldn't use the MBP as an audio output directly. It appeared to be a way to use the phone as a Bluetooth modem but I don't have a SIM for it so I did not try.
There are apps on the Google Play Store that allow Android to use AirPlay (I tried AllCast with dubious success, see http://gizmodo.com/how-to-stream-anything-from-android-to-airplay-1578516449), but this kind of convoluted "solutions" tend to break on each update of the streaming technology.
That said, in combination with the AirPlay software solutions described in this answer, it may work.
Something like this would also theoretically work, just for audio output: https://www.aliexpress.com/item/Junsun-Universal-3-5mm-jack-Bluetooth-Aux-Audio-Receiver-Adapter-Hands-free-Car-Kit-Music-Receiver/32838200156.html
You need to connect a bluetooth device that outputs audio with aux which you connect to your device as a microphone, and you play the sound from the microphone on the device - but at this point, it's probably more sane to just buy a bluetooth speaker
Try Julius, which can turn your Mac into a wireless Bluetooth speaker.