I have had this issue for several days now myself. It started with my iPhone 6s and now on iTunes as well. After digging through old support posts I found a solution that actually worked. I don't know if it will work for everyone but it did for me and hopefully it will for you guys too.
[POSSIBLE] SOLUTION:
1) Log into appleid.apple.com* (I had to log in on my phone browser as the login page is broken on Chrome on PC [at least for me]).
2) Go into the security section and scroll down to "Two-Factor Authentication" and turn it off/disable it.
3) Follow any prompts (it made me create new security questions) and then wait a minute to make sure the change registers.
4) Try logging back in on your devices.
*If you aren't able to log in to the site, your account may be blocked. There are other posts explaining how to fix that.
Hope this helps.