I keep trying to log in using the information for my ESO (PS4) account, but it keeps telling me it's not valid. I try to create another directly on the site, and it keeps talking about an invitation code... is this some kind of joke website, or if it's official, where do I find this code?

It sounds as though Zenimax might be experiencing a few problems with the new launch. There's at least one other person who is having trouble logging onto the forums:

http://www.gamesas.com/topic/1520328-eso/

If it's any consolation these problems are probably temporary. Most MMOs go through these kinds of growing pains after launch day.

These aren't the ESO forums, so we can't help you access them.
I suggest contacting ESO's customer support.

As you likely understand, the ESO forums are invite only. Meaning, you have to own the game before you can join them.
Some people have been saying that the ESO forums are not working correctly for console players, and this is probably due to high traffic and/or a problem with the ESO servers.

Again, your best option is to contact ESO customer support, or try Google and see if someone has found a fix.

Give it a few days, and I suspect the problems will be fixed anyways.