How do I side-load old downloaded podcasts onto an iPhone? Is it even possible?

For complicated reasons outside of the scope of this question, I'm stuck using and carrying an iPhone.  (I know it's not optimal for many purposes, including my current one.)  

A lot of older podcasts (or older episodes of current podcasts) aren't available on iTunes.  Right now, the only way I know to get a podcast into the "Podcasts" app on my iPhone is to find it in iTunes at Apple and download it from within the app.  It used to be possible before podcasts were separated from music to sideload into iTunes on the PC and then synch over, but if that still works I can't figure out how to make it happen.

So, if I have a website with a bunch of old podcasts in MP3 format, what's the best way to get them onto my iPhone to listen to them?  Is there some other app I should be using? Or what?

All suggestions gratefully received.

Dan - I had an mp3 from the 2015 geoff lawton pdc and added it to itunes -(file - add file to library), then created a new playlist in itunes (file - new - playlist), then dragged the pdc mp3 into the new playlist.  then i plugged in my iphone into the computer, waited for itunes to recognize it, then expanded the iphone menu, and then dragged the new playlist onto the iphone item.  Synch notice came up and when it finished, i opened the music icon on the iphone and the new playlist with mp3 file was there.  The above instructions are with a playlist, I also did the same with a single file and it worked as well.  However, if you don't edit the info for the mp3's, they show up in the "Unknown" album and can be hard to find, so once the file is added to itunes, right click on the file and edit the artist, album, and genre at a minimum so the file shows up in the album list.  Itunes is smart enough that you can edit a group of files and enter the same album name and have them all show up under that album.

Let me know if you were able to get the podcasts loaded

cheers
Kevin

Thanks, Kevin, I will try that, but it may be a few days before I report back, I've got a ton of things going on at once and getting my podcasts loaded up is unfortunately not at the top of the list.  

It really frustrates me that I can find mp3 files on the web with my phone but there doesn't seem to be any way to save them in bulk ON my phone to listen later without going through a PC.

Dan - no worries on timeframe, I have that setting turned on so I get emails on threads I post to.

Yes, it's a bummer you can't just download from web to phone, I have a long history of cussing at apple because they limit access to a device I purchased.  I have software that will access other parts of iPhone storage, but still need a pc to do it!!

Kevin