If the recordings are licensed in the public domain, out of copyright, or creative commons, archive.org provides free audio hosting. http://archive.org/about/faqs.php#224
All of the services listed are not a substitute for an offline cold backup, just a reminder. Site content on Amazon or YouTube can disappear because of copyright dispute claims or policy conflicts like Terms of Service violation or other arbitrary policy changes.
Commercial podcast hosting appears to be tiered by upload amount per month; this is a comparison: https://www.thepodcasthost.com/websites-hosting/best-podcast-hosting/
The advantages of some podcast hosting services is that they might have automatically generated RSS feed services, and might provide integration with other podcast syndicators such as rdio.com or stitcher.com. No particular service is better than others at iTunes integration because iirc, iTunes plays by its own rules.
Moving podcast hosting often involves altering podcast feeds which can alter the subscribers content (like flood it with hundreds of ‘unread/new’ items), or make it appear to have stopped updating altogether. It definitely takes some homework to prepare for a move.
Hosting videos can also be done on vimeo.com or anything that hosts files. Video hosting services typically differentiate themselves by their online players (mobile friendly vs High Definition).
Live streaming services are available from both YouTube, vimeo.com, or other services like ScaleEngine.com or Twich. Converting a live stream to a hosted video takes forethought to record the video, sometimes on a separate device.