I'd like to host a game night for friends and family where we play games like jackbox. I'd like to self host the service and give anyone a url and possibly a user name/password combination to access it. I'd like audio and video support as well as the ability to screen share and have a text chat option. I know there are a couple of services that do some of these things but does anyone know of an option that part offers all of this?
It might sound crazy, but nextcloud actually can do all of that. It's pretty easy to activate if you already have a nextcloud instance. Just enable nextcloud talk app on your nextcloud instance, and maybe add a stun/turn server to make it works through double nat.
+1 as a discord replacement though, if op wants all in one then jitsi sounds like the way to go, but if they're looking for a drop in discord replacement revolt has been making progress
Revolt is a matrix-compliant client and server combo. It's easier to deploy than synapse+element but obviously you miss out on some fringe features. There's also the issue that a lot of the hard parts of setting up a matrix server are due to the video part.
Since OP wants video chat and screen share first and foremost, and since revolt and matrix both use jitsi for this, OP can use straight up jitsi and set up matrix/revolt later.